Interactive compound inequalities worksheet with problems, solutions, and number line graphs for classroom learning.

Let's solve each compound inequality step by step, determine the correct solution set, and then match it to the corresponding letter and number line.

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Step 1: Solve Each Inequality

We'll go through each row, solve the compound inequality, and find the matching solution (letter) and number line (number).

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#### 1. $-10 \leq 2x - 4 < -2$

Break into two parts:

- $-10 \leq 2x - 4$ → Add 4: $-6 \leq 2x$ → Divide by 2: $-3 \leq x$
- $2x - 4 < -2$ → Add 4: $2x < 2$ → Divide by 2: $x < 1$

So: $-3 \leq x < 1$

✔ Matches: B ($-3 \leq x < 1$)

Number line: 1 (closed at -3, open at 1)

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#### 2. $2x - 4 \geq 2$ or $-4x + 6 > 2$

Solve each:

- $2x - 4 \geq 2$ → $2x \geq 6$ → $x \geq 3$
- $-4x + 6 > 2$ → $-4x > -4$ → $x < 1$ (inequality flips when dividing by negative)

So: $x < 1$ or $x \geq 3$

✔ Matches: G ($x < 1$ or $x \geq 3$)

Number line: 16 (open at 1, closed at 3, shaded left of 1 and right of 3)

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#### 3. $-5 \leq 4x - 9 < 3$

Break:

- $-5 \leq 4x - 9$ → $4 \leq 4x$ → $x \geq 1$
- $4x - 9 < 3$ → $4x < 12$ → $x < 3$

So: $1 \leq x < 3$

✔ Matches: F ($1 \leq x < 3$)

Number line: 7 (closed at 1, open at 3)

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#### 4. $-6x + 1 > -5$ and $3x + 4 \geq 1$

Solve both:

- $-6x + 1 > -5$ → $-6x > -6$ → $x < 1$
- $3x + 4 \geq 1$ → $3x \geq -3$ → $x \geq -1$

So: $-1 \leq x < 1$

✔ Matches: K ($-1 \leq x < 1$)

Number line: 3 (closed at -1, open at 1)

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#### 5. $-3x + 4 \geq 7$ or $-x - 2 < -5$

Solve:

- $-3x + 4 \geq 7$ → $-3x \geq 3$ → $x \leq -1$
- $-x - 2 < -5$ → $-x < -3$ → $x > 3$

So: $x \leq -1$ or $x > 3$

✔ Matches: J ($x \leq -1$ or $x > 3$)

Number line: 13 (closed at -1, open at 3, shaded left of -1 and right of 3)

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#### 6. $-6 < 4x - 2 \leq 10$

Break:

- $-6 < 4x - 2$ → $-4 < 4x$ → $x > -1$
- $4x - 2 \leq 10$ → $4x \leq 12$ → $x \leq 3$

So: $-1 < x \leq 3$

✔ Matches: N ($-1 < x \leq 3$)

Number line: 6 (open at -1, closed at 3)

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#### 7. $-2x - 3 \geq 3$ or $3x - 4 > -1$

Solve:

- $-2x - 3 \geq 3$ → $-2x \geq 6$ → $x \leq -3$
- $3x - 4 > -1$ → $3x > 3$ → $x > 1$

So: $x \leq -3$ or $x > 1$

✔ Matches: H ($x \leq -3$ or $x > 1$)

Number line: 9 (closed at -3, open at 1, shaded left of -3 and right of 1)

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#### 8. $-2x + 1 \geq -5$ and $2x + 1 > 3$

Solve:

- $-2x + 1 \geq -5$ → $-2x \geq -6$ → $x \leq 3$
- $2x + 1 > 3$ → $2x > 2$ → $x > 1$

So: $1 < x \leq 3$

✔ Matches: I ($1 < x \leq 3$)

Number line: 8 (open at 1, closed at 3)

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#### 9. $-x + 4 \geq 3$ and $-2x + 3 < 9$

Solve:

- $-x + 4 \geq 3$ → $-x \geq -1$ → $x \leq 1$
- $-2x + 3 < 9$ → $-2x < 6$ → $x > -3$

So: $-3 < x \leq 1$

✔ Matches: M ($-3 < x \leq 1$)

Number line: 2 (open at -3, closed at 1)

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#### 10. $5x + 3 \leq -2$ or $-4x + 5 < 1$

Solve:

- $5x + 3 \leq -2$ → $5x \leq -5$ → $x \leq -1$
- $-4x + 5 < 1$ → $-4x < -4$ → $x > 1$

So: $x \leq -1$ or $x > 1$

✔ Matches: O ($x \leq -1$ or $x > 1$)

Number line: 11 (closed at -1, open at 1, shaded left of -1 and right of 1)

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#### 11. $-5x + 6 < -9$ or $6x - 4 \leq 2$

Solve:

- $-5x + 6 < -9$ → $-5x < -15$ → $x > 3$
- $6x - 4 \leq 2$ → $6x \leq 6$ → $x \leq 1$

So: $x \leq 1$ or $x > 3$

✔ Matches: L ($x \leq 1$ or $x > 3$)

Number line: 15 (closed at 1, open at 3, shaded left of 1 and right of 3)

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#### 12. $1 < 3x + 4 \leq 7$

Break:

- $1 < 3x + 4$ → $-3 < 3x$ → $x > -1$
- $3x + 4 \leq 7$ → $3x \leq 3$ → $x \leq 1$

So: $-1 < x \leq 1$

✔ Matches: P ($-1 < x \leq 1$)

Number line: 4 (open at -1, closed at 1)

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#### 13. $-3x + 5 \leq 2$ or $2x + 9 < 3$

Solve:

- $-3x + 5 \leq 2$ → $-3x \leq -3$ → $x \geq 1$
- $2x + 9 < 3$ → $2x < -6$ → $x < -3$

So: $x < -3$ or $x \geq 1$

✔ Matches: D ($x < -3$ or $x \geq 1$)

Number line: 10 (open at -3, closed at 1, shaded left of -3 and right of 1)

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#### 14. $-3x + 5 \leq 2$ or $4x - 2 < -6$

Wait — this is similar to above but second inequality different.

- $-3x + 5 \leq 2$ → $x \geq 1$
- $4x - 2 < -6$ → $4x < -4$ → $x < -1$

So: $x < -1$ or $x \geq 1$

✔ Matches: E ($x < -1$ or $x \geq 1$)

Number line: 12 (open at -1, closed at 1, shaded left of -1 and right of 1)

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#### 15. $1 \leq 3x + 4 < 13$

Break:

- $1 \leq 3x + 4$ → $-3 \leq 3x$ → $x \geq -1$
- $3x + 4 < 13$ → $3x < 9$ → $x < 3$

So: $-1 \leq x < 3$

✔ Matches: C ($-1 \leq x < 3$)

Number line: 5 (closed at -1, open at 3)

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#### 16. $-2x + 1 > 3$ or $-3x + 4 \leq -5$

Solve:

- $-2x + 1 > 3$ → $-2x > 2$ → $x < -1$
- $-3x + 4 \leq -5$ → $-3x \leq -9$ → $x \geq 3$

So: $x < -1$ or $x \geq 3$

✔ Matches: A ($x < -1$ or $x \geq 3$)

Number line: 14 (open at -1, closed at 3, shaded left of -1 and right of 3)

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✔ Final Matching Table

| Problem | Solution | Letter | Number Line |
|--------|----------|--------|-------------|
| 1 | $-3 \leq x < 1$ | B | 1 |
| 2 | $x < 1$ or $x \geq 3$ | G | 16 |
| 3 | $1 \leq x < 3$ | F | 7 |
| 4 | $-1 \leq x < 1$ | K | 3 |
| 5 | $x \leq -1$ or $x > 3$ | J | 13 |
| 6 | $-1 < x \leq 3$ | N | 6 |
| 7 | $x \leq -3$ or $x > 1$ | H | 9 |
| 8 | $1 < x \leq 3$ | I | 8 |
| 9 | $-3 < x \leq 1$ | M | 2 |
| 10 | $x \leq -1$ or $x > 1$ | O | 11 |
| 11 | $x \leq 1$ or $x > 3$ | L | 15 |
| 12 | $-1 < x \leq 1$ | P | 4 |
| 13 | $x < -3$ or $x \geq 1$ | D | 10 |
| 14 | $x < -1$ or $x \geq 1$ | E | 12 |
| 15 | $-1 \leq x < 3$ | C | 5 |
| 16 | $x < -1$ or $x \geq 3$ | A | 14 |

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📌 Summary of Answers:

Each compound inequality matches as follows:

1. B, 1
2. G, 16
3. F, 7
4. K, 3
5. J, 13
6. N, 6
7. H, 9
8. I, 8
9. M, 2
10. O, 11
11. L, 15
12. P, 4
13. D, 10
14. E, 12
15. C, 5
16. A, 14

This completes the matching! Let me know if you'd like a printable version or explanation for any specific one.