Absolute Value Equations Coloring Activity - Free Printable

Let's solve each of the absolute value equations step by step. Since this is a coloring worksheet, we need to find the solution(s) for each equation, which will be used to match a color key (not provided here). But I’ll solve each one completely so you can proceed with coloring.

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1. |5x| = 15

Break into two cases:

- Case 1: $5x = 15$ → $x = 3$
- Case 2: $5x = -15$ → $x = -3$

✔ Solutions: $x = 3$ or $x = -3$

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2. |-2x| = 8

Note: $|-2x| = |2x|$, so we can write:

- $2x = 8$ → $x = 4$
- $2x = -8$ → $x = -4$

✔ Solutions: $x = 4$ or $x = -4$

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3. |x/4| = 24

Multiply both sides by 4:

- $|x| = 96$

Then:
- $x = 96$ or $x = -96$

✔ Solutions: $x = 96$ or $x = -96$

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4. |x - 7| = 10

Two cases:

- $x - 7 = 10$ → $x = 17$
- $x - 7 = -10$ → $x = -3$

✔ Solutions: $x = 17$ or $x = -3$

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5. |x + 2| + 3 = 7

Subtract 3 from both sides:

- $|x + 2| = 4$

Now solve:

- $x + 2 = 4$ → $x = 2$
- $x + 2 = -4$ → $x = -6$

✔ Solutions: $x = 2$ or $x = -6$

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6. 5|x/2| = 20

Divide both sides by 5:

- $|x/2| = 4$

Multiply both sides by 2:

- $|x| = 8$

So:
- $x = 8$ or $x = -8$

✔ Solutions: $x = 8$ or $x = -8$

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7. |3x| - 5 = 10

Add 5 to both sides:

- $|3x| = 15$

Then:
- $3x = 15$ → $x = 5$
- $3x = -15$ → $x = -5$

✔ Solutions: $x = 5$ or $x = -5$

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8. |-2x + 6| = 6

Set up two cases:

- $-2x + 6 = 6$ → $-2x = 0$ → $x = 0$
- $-2x + 6 = -6$ → $-2x = -12$ → $x = 6$

✔ Solutions: $x = 0$ or $x = 6$

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9. 2|4x + 1| = 10

Divide both sides by 2:

- $|4x + 1| = 5$

Now solve:

- $4x + 1 = 5$ → $4x = 4$ → $x = 1$
- $4x + 1 = -5$ → $4x = -6$ → $x = -\frac{3}{2}$

✔ Solutions: $x = 1$ or $x = -\frac{3}{2}$

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10. 2 - |3x - 9| = 2

Subtract 2 from both sides:

- $-|3x - 9| = 0$

Multiply both sides by -1:

- $|3x - 9| = 0$

Absolute value equals zero only when expression inside is zero:

- $3x - 9 = 0$ → $3x = 9$ → $x = 3$

✔ Solution: $x = 3$

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✔ Final Answers Summary:

| Problem | Solution(s) |
|--------|-------------|
| 1 | $x = 3$, $x = -3$ |
| 2 | $x = 4$, $x = -4$ |
| 3 | $x = 96$, $x = -96$ |
| 4 | $x = 17$, $x = -3$ |
| 5 | $x = 2$, $x = -6$ |
| 6 | $x = 8$, $x = -8$ |
| 7 | $x = 5$, $x = -5$ |
| 8 | $x = 0$, $x = 6$ |
| 9 | $x = 1$, $x = -\frac{3}{2}$ |
| 10 | $x = 3$ |

> 🎨 Now, use these answers to look up the corresponding color on the coloring key page (which isn't shown here), and color in the picture accordingly using the problem number and matching color.

Let me know if you'd like help interpreting the color key or creating a visual guide!