Worksheet for solving compound inequalities, matching each problem to its correct solution and number line representation.

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

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

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

✔ Solution: B: $-3 \leq x < 1$
Number line: 1

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

Solve each:
- $2x - 4 \geq 2$: $2x \geq 6$, so $x \geq 3$
- $-4x + 6 > 2$: $-4x > -4$, divide by -4 → reverse inequality: $x < 1$

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

✔ Solution: G: $x < 1$ or $x \geq 3$
Number line: 16

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

Add 9: $4 \leq 4x < 12$
Divide by 4: $1 \leq x < 3$

✔ Solution: F: $1 \leq x < 3$
Number line: 7

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

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

So: $-1 \leq x < 1$

✔ Solution: K: $-1 \leq x < 1$
Number line: 3

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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 $x > 3$

✔ Solution: J: $x \leq -1$ or $x > 3$
Number line: 13

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

Add 2: $-4 < 4x \leq 12$
Divide by 4: $-1 < x \leq 3$

✔ Solution: N: $-1 < x \leq 3$
Number line: 6

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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 $x > 1$

✔ Solution: H: $x \leq -3$ or $x > 1$
Number line: 9

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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: $1 < x \leq 3$

✔ Solution: I: $1 < x \leq 3$
Number line: 8

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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: $-3 < x \leq 1$

✔ Solution: M: $-3 < x \leq 1$
Number line: 2

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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 $x > 1$

✔ Solution: O: $x \leq -1$ or $x > 1$
Number line: 11

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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 $x > 3$

✔ Solution: L: $x \leq 1$ or $x > 3$
Number line: 15

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

Subtract 4: $-3 < 3x \leq 3$
Divide by 3: $-1 < x \leq 1$

✔ Solution: P: $-1 < x \leq 1$
Number line: 4

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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 $x \geq 1$

✔ Solution: D: $x < -3$ or $x \geq 1$
Number line: 10

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

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

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

✔ Solution: E: $x < -1$ or $x \geq 1$
Number line: 12

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

Subtract 4: $-3 \leq 3x < 9$
Divide by 3: $-1 \leq x < 3$

✔ Solution: C: $-1 \leq x < 3$
Number line: 5

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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 $x \geq 3$

✔ Solution: A: $x < -1$ or $x \geq 3$
Number line: 14

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✔ Final Matching Summary:

| Inequality | Letter | Number Line |
|-----------|--------|-------------|
| 1. $-10 \leq 2x-4 < -2$ | B | 1 |
| 2. $2x-4\geq2$ or $-4x+6>2$ | G | 16 |
| 3. $-5\leq4x-9<3$ | F | 7 |
| 4. $-6x+1>-5$ and $3x+4\geq1$ | K | 3 |
| 5. $-3x+4\geq7$ or $-x-2<-5$ | J | 13 |
| 6. $-6<4x-2\leq10$ | N | 6 |
| 7. $-2x-3\geq3$ or $3x-4>-1$ | H | 9 |
| 8. $-2x+1\geq-5$ and $2x+1>3$ | I | 8 |
| 9. $-x+4\geq3$ and $-2x+3<9$ | M | 2 |
|10. $5x+3\leq-2$ or $-4x+5<1$ | O | 11 |
|11. $-5x+6<-9$ or $6x-4\leq2$ | L | 15 |
|12. $1<3x+4\leq7$ | P | 4 |
|13. $-3x+5\leq2$ or $2x+9<3$ | D | 10 |
|14. $-3x+5\leq2$ or $4x-2<-6$ | E | 12 |
|15. $1\leq3x+4<13$ | C | 5 |
|16. $-2x+1>3$ or $-3x+4\leq-5$ | A | 14 |

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✔ Final Answer:

All inequalities are correctly solved and matched.

You can now use this table to fill in the matching on your worksheet.

Let me know if you'd like a printable version or visual explanation!