Content review: I Spy the Inequality
Status: Published — approved by the creator. Mastery threshold 80% (provisional).
Challenge 1 of 10
Find the clue
You may bring no more than 4 guests. Let x be the number of guests.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. You
- W1. may
- W2. bring
- W3. no more than ✓
- W4. 4
- W5. guests.
- W6. Let
- W7. x
- W8. be
- W9. the
- W10. number
- W11. of
- W12. guests.
Answer: no more than
✓ Correct: You found “no more than.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W4: 4 is the boundary number. Tap the words that compare x with it.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
✗ If W11: Not that word. Look for language that sets a limit or comparison.
✗ If W12: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 4?
- LT. <
- LE. ≤ ✓
- GT. >
- GE. ≥
Answer: ≤
✓ Correct: Yes! x ≤ 4.
✗ If LT: Try again. “no more than 4” includes 4 itself, so the symbol needs the line underneath.
✗ If GT: Try again. “no more than 4” means values smaller than 4. Check which way the symbol opens. “no more than 4” includes 4 itself, so the symbol needs the line underneath.
✗ If GE: Try again. “no more than 4” means values smaller than 4. Check which way the symbol opens.
Step 3 · Match the number line
Which number line matches x ≤ 4?
- OL. Open circle at 4, shaded left
- CL. Closed circle at 4, shaded left ✓
- OR. Open circle at 4, shaded right
- CR. Closed circle at 4, shaded right
Answer: Closed circle at 4, shaded left
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. An open circle leaves 4 out, but x ≤ 4 includes 4.
✗ If OR: Try again. An open circle leaves 4 out, but x ≤ 4 includes 4. x ≤ 4 uses values less than 4, so shade to the left.
✗ If CR: Try again. x ≤ 4 uses values less than 4, so shade to the left.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 4, shaded left
- SL. Solid vertical line at x = 4, shaded left ✓
- DR. Dashed vertical line at x = 4, shaded right
- SR. Solid vertical line at x = 4, shaded right
Answer: Solid vertical line at x = 4, shaded left
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. A dashed boundary leaves out points on x = 4, but x ≤ 4 includes them.
✗ If DR: Try again. A dashed boundary leaves out points on x = 4, but x ≤ 4 includes them. x ≤ 4 uses values less than 4, so shade to the left.
✗ If SR: Try again. x ≤ 4 uses values less than 4, so shade to the left.
Challenge 2 of 10
Find the clue
You need at least 2 tickets. Let x be the number of tickets.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. You
- W1. need
- W2. at least ✓
- W3. 2
- W4. tickets.
- W5. Let
- W6. x
- W7. be
- W8. the
- W9. number
- W10. of
- W11. tickets.
Answer: at least
✓ Correct: You found “at least.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W3: 2 is the boundary number. Tap the words that compare x with it.
✗ If W4: Not that word. Look for language that sets a limit or comparison.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
✗ If W11: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 2?
- LT. <
- LE. ≤
- GT. >
- GE. ≥ ✓
Answer: ≥
✓ Correct: Yes! x ≥ 2.
✗ If LT: Try again. “at least 2” means values larger than 2. Check which way the symbol opens. “at least 2” includes 2 itself, so the symbol needs the line underneath.
✗ If LE: Try again. “at least 2” means values larger than 2. Check which way the symbol opens.
✗ If GT: Try again. “at least 2” includes 2 itself, so the symbol needs the line underneath.
Step 3 · Match the number line
Which number line matches x ≥ 2?
- OL. Open circle at 2, shaded left
- CL. Closed circle at 2, shaded left
- OR. Open circle at 2, shaded right
- CR. Closed circle at 2, shaded right ✓
Answer: Closed circle at 2, shaded right
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. An open circle leaves 2 out, but x ≥ 2 includes 2. x ≥ 2 uses values greater than 2, so shade to the right.
✗ If CL: Try again. x ≥ 2 uses values greater than 2, so shade to the right.
✗ If OR: Try again. An open circle leaves 2 out, but x ≥ 2 includes 2.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 2, shaded left
- SL. Solid vertical line at x = 2, shaded left
- DR. Dashed vertical line at x = 2, shaded right
- SR. Solid vertical line at x = 2, shaded right ✓
Answer: Solid vertical line at x = 2, shaded right
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. A dashed boundary leaves out points on x = 2, but x ≥ 2 includes them. x ≥ 2 uses values greater than 2, so shade to the right.
✗ If SL: Try again. x ≥ 2 uses values greater than 2, so shade to the right.
✗ If DR: Try again. A dashed boundary leaves out points on x = 2, but x ≥ 2 includes them.
Challenge 3 of 10
Find the clue
A team has fewer than 6 members. Let x be the number of members.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. A
- W1. team
- W2. has
- W3. fewer than ✓
- W4. 6
- W5. members.
- W6. Let
- W7. x
- W8. be
- W9. the
- W10. number
- W11. of
- W12. members.
Answer: fewer than
✓ Correct: You found “fewer than.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W4: 6 is the boundary number. Tap the words that compare x with it.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
✗ If W11: Not that word. Look for language that sets a limit or comparison.
✗ If W12: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 6?
- LT. < ✓
- LE. ≤
- GT. >
- GE. ≥
Answer: <
✓ Correct: Yes! x < 6.
✗ If LE: Try again. “fewer than 6” leaves 6 out, so the symbol should not have the line underneath.
✗ If GT: Try again. “fewer than 6” means values smaller than 6. Check which way the symbol opens.
✗ If GE: Try again. “fewer than 6” means values smaller than 6. Check which way the symbol opens. “fewer than 6” leaves 6 out, so the symbol should not have the line underneath.
Step 3 · Match the number line
Which number line matches x < 6?
- OL. Open circle at 6, shaded left ✓
- CL. Closed circle at 6, shaded left
- OR. Open circle at 6, shaded right
- CR. Closed circle at 6, shaded right
Answer: Open circle at 6, shaded left
✓ Correct: Yes! The endpoint and direction match.
✗ If CL: Try again. A closed circle includes 6, but x < 6 leaves 6 out.
✗ If OR: Try again. x < 6 uses values less than 6, so shade to the left.
✗ If CR: Try again. A closed circle includes 6, but x < 6 leaves 6 out. x < 6 uses values less than 6, so shade to the left.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 6, shaded left ✓
- SL. Solid vertical line at x = 6, shaded left
- DR. Dashed vertical line at x = 6, shaded right
- SR. Solid vertical line at x = 6, shaded right
Answer: Dashed vertical line at x = 6, shaded left
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If SL: Try again. A solid boundary includes points on x = 6, but x < 6 leaves them out.
✗ If DR: Try again. x < 6 uses values less than 6, so shade to the left.
✗ If SR: Try again. A solid boundary includes points on x = 6, but x < 6 leaves them out. x < 6 uses values less than 6, so shade to the left.
Challenge 4 of 10
Find the clue
You earned more than 3 points. Let x be the points earned.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. You
- W1. earned
- W2. more than ✓
- W3. 3
- W4. points.
- W5. Let
- W6. x
- W7. be
- W8. the
- W9. points
- W10. earned.
Answer: more than
✓ Correct: You found “more than.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W3: 3 is the boundary number. Tap the words that compare x with it.
✗ If W4: Not that word. Look for language that sets a limit or comparison.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 3?
- LT. <
- LE. ≤
- GT. > ✓
- GE. ≥
Answer: >
✓ Correct: Yes! x > 3.
✗ If LT: Try again. “more than 3” means values larger than 3. Check which way the symbol opens.
✗ If LE: Try again. “more than 3” means values larger than 3. Check which way the symbol opens. “more than 3” leaves 3 out, so the symbol should not have the line underneath.
✗ If GE: Try again. “more than 3” leaves 3 out, so the symbol should not have the line underneath.
Step 3 · Match the number line
Which number line matches x > 3?
- OL. Open circle at 3, shaded left
- CL. Closed circle at 3, shaded left
- OR. Open circle at 3, shaded right ✓
- CR. Closed circle at 3, shaded right
Answer: Open circle at 3, shaded right
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. x > 3 uses values greater than 3, so shade to the right.
✗ If CL: Try again. A closed circle includes 3, but x > 3 leaves 3 out. x > 3 uses values greater than 3, so shade to the right.
✗ If CR: Try again. A closed circle includes 3, but x > 3 leaves 3 out.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 3, shaded left
- SL. Solid vertical line at x = 3, shaded left
- DR. Dashed vertical line at x = 3, shaded right ✓
- SR. Solid vertical line at x = 3, shaded right
Answer: Dashed vertical line at x = 3, shaded right
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. x > 3 uses values greater than 3, so shade to the right.
✗ If SL: Try again. A solid boundary includes points on x = 3, but x > 3 leaves them out. x > 3 uses values greater than 3, so shade to the right.
✗ If SR: Try again. A solid boundary includes points on x = 3, but x > 3 leaves them out.
Challenge 5 of 10
Find the clue
The bag holds a maximum of 5 books. Let x be the number of books.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. The
- W1. bag
- W2. holds
- W3. a maximum of ✓
- W4. 5
- W5. books.
- W6. Let
- W7. x
- W8. be
- W9. the
- W10. number
- W11. of
- W12. books.
Answer: a maximum of
✓ Correct: You found “a maximum of.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W4: 5 is the boundary number. Tap the words that compare x with it.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
✗ If W11: Not that word. Look for language that sets a limit or comparison.
✗ If W12: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 5?
- LT. <
- LE. ≤ ✓
- GT. >
- GE. ≥
Answer: ≤
✓ Correct: Yes! x ≤ 5.
✗ If LT: Try again. “a maximum of 5” includes 5 itself, so the symbol needs the line underneath.
✗ If GT: Try again. “a maximum of 5” means values smaller than 5. Check which way the symbol opens. “a maximum of 5” includes 5 itself, so the symbol needs the line underneath.
✗ If GE: Try again. “a maximum of 5” means values smaller than 5. Check which way the symbol opens.
Step 3 · Match the number line
Which number line matches x ≤ 5?
- OL. Open circle at 5, shaded left
- CL. Closed circle at 5, shaded left ✓
- OR. Open circle at 5, shaded right
- CR. Closed circle at 5, shaded right
Answer: Closed circle at 5, shaded left
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. An open circle leaves 5 out, but x ≤ 5 includes 5.
✗ If OR: Try again. An open circle leaves 5 out, but x ≤ 5 includes 5. x ≤ 5 uses values less than 5, so shade to the left.
✗ If CR: Try again. x ≤ 5 uses values less than 5, so shade to the left.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 5, shaded left
- SL. Solid vertical line at x = 5, shaded left ✓
- DR. Dashed vertical line at x = 5, shaded right
- SR. Solid vertical line at x = 5, shaded right
Answer: Solid vertical line at x = 5, shaded left
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. A dashed boundary leaves out points on x = 5, but x ≤ 5 includes them.
✗ If DR: Try again. A dashed boundary leaves out points on x = 5, but x ≤ 5 includes them. x ≤ 5 uses values less than 5, so shade to the left.
✗ If SR: Try again. x ≤ 5 uses values less than 5, so shade to the left.
Challenge 6 of 10
Find the clue
The ride requires a minimum of 1 token. Let x be the number of tokens.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. The
- W1. ride
- W2. requires
- W3. a minimum of ✓
- W4. 1
- W5. token.
- W6. Let
- W7. x
- W8. be
- W9. the
- W10. number
- W11. of
- W12. tokens.
Answer: a minimum of
✓ Correct: You found “a minimum of.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W4: 1 is the boundary number. Tap the words that compare x with it.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
✗ If W11: Not that word. Look for language that sets a limit or comparison.
✗ If W12: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 1?
- LT. <
- LE. ≤
- GT. >
- GE. ≥ ✓
Answer: ≥
✓ Correct: Yes! x ≥ 1.
✗ If LT: Try again. “a minimum of 1” means values larger than 1. Check which way the symbol opens. “a minimum of 1” includes 1 itself, so the symbol needs the line underneath.
✗ If LE: Try again. “a minimum of 1” means values larger than 1. Check which way the symbol opens.
✗ If GT: Try again. “a minimum of 1” includes 1 itself, so the symbol needs the line underneath.
Step 3 · Match the number line
Which number line matches x ≥ 1?
- OL. Open circle at 1, shaded left
- CL. Closed circle at 1, shaded left
- OR. Open circle at 1, shaded right
- CR. Closed circle at 1, shaded right ✓
Answer: Closed circle at 1, shaded right
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. An open circle leaves 1 out, but x ≥ 1 includes 1. x ≥ 1 uses values greater than 1, so shade to the right.
✗ If CL: Try again. x ≥ 1 uses values greater than 1, so shade to the right.
✗ If OR: Try again. An open circle leaves 1 out, but x ≥ 1 includes 1.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 1, shaded left
- SL. Solid vertical line at x = 1, shaded left
- DR. Dashed vertical line at x = 1, shaded right
- SR. Solid vertical line at x = 1, shaded right ✓
Answer: Solid vertical line at x = 1, shaded right
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. A dashed boundary leaves out points on x = 1, but x ≥ 1 includes them. x ≥ 1 uses values greater than 1, so shade to the right.
✗ If SL: Try again. x ≥ 1 uses values greater than 1, so shade to the right.
✗ If DR: Try again. A dashed boundary leaves out points on x = 1, but x ≥ 1 includes them.
Challenge 7 of 10
Find the clue
The temperature is below 0°. Let x be the temperature.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. The
- W1. temperature
- W2. is
- W3. below ✓
- W4. 0°.
- W5. Let
- W6. x
- W7. be
- W8. the
- W9. temperature.
Answer: below
✓ Correct: You found “below.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W4: 0° is the boundary number. Tap the words that compare x with it.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 0?
- LT. < ✓
- LE. ≤
- GT. >
- GE. ≥
Answer: <
✓ Correct: Yes! x < 0.
✗ If LE: Try again. “below 0” leaves 0 out, so the symbol should not have the line underneath.
✗ If GT: Try again. “below 0” means values smaller than 0. Check which way the symbol opens.
✗ If GE: Try again. “below 0” means values smaller than 0. Check which way the symbol opens. “below 0” leaves 0 out, so the symbol should not have the line underneath.
Step 3 · Match the number line
Which number line matches x < 0?
- OL. Open circle at 0, shaded left ✓
- CL. Closed circle at 0, shaded left
- OR. Open circle at 0, shaded right
- CR. Closed circle at 0, shaded right
Answer: Open circle at 0, shaded left
✓ Correct: Yes! The endpoint and direction match.
✗ If CL: Try again. A closed circle includes 0, but x < 0 leaves 0 out.
✗ If OR: Try again. x < 0 uses values less than 0, so shade to the left.
✗ If CR: Try again. A closed circle includes 0, but x < 0 leaves 0 out. x < 0 uses values less than 0, so shade to the left.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 0, shaded left ✓
- SL. Solid vertical line at x = 0, shaded left
- DR. Dashed vertical line at x = 0, shaded right
- SR. Solid vertical line at x = 0, shaded right
Answer: Dashed vertical line at x = 0, shaded left
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If SL: Try again. A solid boundary includes points on x = 0, but x < 0 leaves them out.
✗ If DR: Try again. x < 0 uses values less than 0, so shade to the left.
✗ If SR: Try again. A solid boundary includes points on x = 0, but x < 0 leaves them out. x < 0 uses values less than 0, so shade to the left.
Challenge 8 of 10
Find the clue
You can spend up to $7. Let x be the dollars spent.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. You
- W1. can
- W2. spend
- W3. up to ✓
- W4. $7.
- W5. Let
- W6. x
- W7. be
- W8. the
- W9. dollars
- W10. spent.
Answer: up to
✓ Correct: You found “up to.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W4: $7 is the boundary number. Tap the words that compare x with it.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 7?
- LT. <
- LE. ≤ ✓
- GT. >
- GE. ≥
Answer: ≤
✓ Correct: Yes! x ≤ 7.
✗ If LT: Try again. “up to 7” includes 7 itself, so the symbol needs the line underneath.
✗ If GT: Try again. “up to 7” means values smaller than 7. Check which way the symbol opens. “up to 7” includes 7 itself, so the symbol needs the line underneath.
✗ If GE: Try again. “up to 7” means values smaller than 7. Check which way the symbol opens.
Step 3 · Match the number line
Which number line matches x ≤ 7?
- OL. Open circle at 7, shaded left
- CL. Closed circle at 7, shaded left ✓
- OR. Open circle at 7, shaded right
- CR. Closed circle at 7, shaded right
Answer: Closed circle at 7, shaded left
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. An open circle leaves 7 out, but x ≤ 7 includes 7.
✗ If OR: Try again. An open circle leaves 7 out, but x ≤ 7 includes 7. x ≤ 7 uses values less than 7, so shade to the left.
✗ If CR: Try again. x ≤ 7 uses values less than 7, so shade to the left.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 7, shaded left
- SL. Solid vertical line at x = 7, shaded left ✓
- DR. Dashed vertical line at x = 7, shaded right
- SR. Solid vertical line at x = 7, shaded right
Answer: Solid vertical line at x = 7, shaded left
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. A dashed boundary leaves out points on x = 7, but x ≤ 7 includes them.
✗ If DR: Try again. A dashed boundary leaves out points on x = 7, but x ≤ 7 includes them. x ≤ 7 uses values less than 7, so shade to the left.
✗ If SR: Try again. x ≤ 7 uses values less than 7, so shade to the left.
Challenge 9 of 10
Find the clue
A passing score is no less than 4. Let x be the score.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. A
- W1. passing
- W2. score
- W3. is
- W4. no less than ✓
- W5. 4.
- W6. Let
- W7. x
- W8. be
- W9. the
- W10. score.
Answer: no less than
✓ Correct: You found “no less than.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W3: Not that word. Look for language that sets a limit or comparison.
✗ If W5: 4 is the boundary number. Tap the words that compare x with it.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 4?
- LT. <
- LE. ≤
- GT. >
- GE. ≥ ✓
Answer: ≥
✓ Correct: Yes! x ≥ 4.
✗ If LT: Try again. “no less than 4” means values larger than 4. Check which way the symbol opens. “no less than 4” includes 4 itself, so the symbol needs the line underneath.
✗ If LE: Try again. “no less than 4” means values larger than 4. Check which way the symbol opens.
✗ If GT: Try again. “no less than 4” includes 4 itself, so the symbol needs the line underneath.
Step 3 · Match the number line
Which number line matches x ≥ 4?
- OL. Open circle at 4, shaded left
- CL. Closed circle at 4, shaded left
- OR. Open circle at 4, shaded right
- CR. Closed circle at 4, shaded right ✓
Answer: Closed circle at 4, shaded right
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. An open circle leaves 4 out, but x ≥ 4 includes 4. x ≥ 4 uses values greater than 4, so shade to the right.
✗ If CL: Try again. x ≥ 4 uses values greater than 4, so shade to the right.
✗ If OR: Try again. An open circle leaves 4 out, but x ≥ 4 includes 4.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 4, shaded left
- SL. Solid vertical line at x = 4, shaded left
- DR. Dashed vertical line at x = 4, shaded right
- SR. Solid vertical line at x = 4, shaded right ✓
Answer: Solid vertical line at x = 4, shaded right
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. A dashed boundary leaves out points on x = 4, but x ≥ 4 includes them. x ≥ 4 uses values greater than 4, so shade to the right.
✗ If SL: Try again. x ≥ 4 uses values greater than 4, so shade to the right.
✗ If DR: Try again. A dashed boundary leaves out points on x = 4, but x ≥ 4 includes them.
Challenge 10 of 10
Find the clue
The height is above 2 meters. Let x be the height.
Input x: → Output :
From original
- Sentence, clue phrase, boundary number and symbol key
- Step order (clue → symbol → number line → coordinate graph) and option order
- Correct-answer feedback and the base wrong-answer messages
- Clue board and worked example
⚠ Reconstructed — needs approval
- Phrase shown as one tappable unit (creator request)
- Pictures as the number-line and graph choices (creator request)
- Choice-specific wrong-answer feedback and mistake labels
- Real-world check note
- Boundary-number tap feedback
Step 1 · Find the inequality clue
Tap the word or phrase in the problem that signals an inequality.
- W0. The
- W1. height
- W2. is
- W3. above ✓
- W4. 2
- W5. meters.
- W6. Let
- W7. x
- W8. be
- W9. the
- W10. height.
Answer: above
✓ Correct: You found “above.” Now choose the symbol.
✗ If W0: Not that word. Look for language that sets a limit or comparison.
✗ If W1: Not that word. Look for language that sets a limit or comparison.
✗ If W2: Not that word. Look for language that sets a limit or comparison.
✗ If W4: 2 is the boundary number. Tap the words that compare x with it.
✗ If W5: Not that word. Look for language that sets a limit or comparison.
✗ If W6: Not that word. Look for language that sets a limit or comparison.
✗ If W7: Not that word. Look for language that sets a limit or comparison.
✗ If W8: Not that word. Look for language that sets a limit or comparison.
✗ If W9: Not that word. Look for language that sets a limit or comparison.
✗ If W10: Not that word. Look for language that sets a limit or comparison.
Step 2 · Choose the symbol
Which symbol completes x __ 2?
- LT. <
- LE. ≤
- GT. > ✓
- GE. ≥
Answer: >
✓ Correct: Yes! x > 2.
✗ If LT: Try again. “above 2” means values larger than 2. Check which way the symbol opens.
✗ If LE: Try again. “above 2” means values larger than 2. Check which way the symbol opens. “above 2” leaves 2 out, so the symbol should not have the line underneath.
✗ If GE: Try again. “above 2” leaves 2 out, so the symbol should not have the line underneath.
Step 3 · Match the number line
Which number line matches x > 2?
- OL. Open circle at 2, shaded left
- CL. Closed circle at 2, shaded left
- OR. Open circle at 2, shaded right ✓
- CR. Closed circle at 2, shaded right
Answer: Open circle at 2, shaded right
✓ Correct: Yes! The endpoint and direction match.
✗ If OL: Try again. x > 2 uses values greater than 2, so shade to the right.
✗ If CL: Try again. A closed circle includes 2, but x > 2 leaves 2 out. x > 2 uses values greater than 2, so shade to the right.
✗ If CR: Try again. A closed circle includes 2, but x > 2 leaves 2 out.
Step 4 · Match the coordinate graph
On the coordinate graph, choose the boundary and shading.
- DL. Dashed vertical line at x = 2, shaded left
- SL. Solid vertical line at x = 2, shaded left
- DR. Dashed vertical line at x = 2, shaded right ✓
- SR. Solid vertical line at x = 2, shaded right
Answer: Dashed vertical line at x = 2, shaded right
✓ Correct: Yes! The graph shows every ordered pair whose x-value works.
✗ If DL: Try again. x > 2 uses values greater than 2, so shade to the right.
✗ If SL: Try again. A solid boundary includes points on x = 2, but x > 2 leaves them out. x > 2 uses values greater than 2, so shade to the right.
✗ If SR: Try again. A solid boundary includes points on x = 2, but x > 2 leaves them out.
Final independent mastery check
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