50+ Absolute Value worksheets for 1st Class on Quizizz | Free ... - Free Printable

Let's solve each of the absolute value problems step by step and identify the correct answers.

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1. $ |3x + 5| = 2 $

The absolute value equation $ |A| = B $ means $ A = B $ or $ A = -B $.

So:
$$
3x + 5 = 2 \quad \text{or} \quad 3x + 5 = -2
$$

Solve each:

- $ 3x + 5 = 2 $ → $ 3x = -3 $ → $ x = -1 $
- $ 3x + 5 = -2 $ → $ 3x = -7 $ → $ x = -\frac{7}{3} $

So, $ x = -1, -\frac{7}{3} $

✔ Answer: B → $ x = -\frac{7}{3}, -1 $

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2. $ |x| < 4 $

This means $ x $ is less than 4 units from 0 on the number line.

So:
$$
-4 < x < 4
$$

✔ Answer: A → $ -4 < x < 4 $

(Note: Option B says $ -4 > x < 4 $, which is invalid syntax.)

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3. $ |5 - 3x| < 1 $

We solve the inequality:
$$
-1 < 5 - 3x < 1
$$

Subtract 5:
$$
-6 < -3x < -4
$$

Divide by -3 (remember to reverse inequalities when dividing by negative):

$$
2 > x > \frac{4}{3}
\quad \Rightarrow \quad \frac{4}{3} < x < 2
$$

✔ Answer: B → $ \frac{4}{3} < x < 2 $

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4. $ |x + 3| = 2 $

Then:
$$
x + 3 = 2 \quad \text{or} \quad x + 3 = -2
$$

- $ x = -1 $
- $ x = -5 $

So $ x = -5, -1 $

✔ Answer: C → $ x = -5, -1 $

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5. $ |5 - 6x| + 2 = 3 $

Subtract 2:
$$
|5 - 6x| = 1
$$

Now solve:
$$
5 - 6x = 1 \quad \text{or} \quad 5 - 6x = -1
$$

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

So $ x = \frac{2}{3}, 1 $

✔ Answer: C → $ x = \frac{2}{3}, 1 $

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6. $ |1 - 4x + 3| - 2 = -2 $

First simplify inside:
$$
|4 - 4x| - 2 = -2
$$

Add 2:
$$
|4 - 4x| = 0
$$

Absolute value is zero only when expression is zero:
$$
4 - 4x = 0 \Rightarrow x = 1
$$

✔ Answer: A → $ x = 1 $

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7. $ |x - 10 + 3x + 5| - 1 < 5 $

Simplify inside:
$$
|4x - 5| - 1 < 5
$$

Add 1:
$$
|4x - 5| < 6
$$

Now solve:
$$
-6 < 4x - 5 < 6
$$

Add 5:
$$
-1 < 4x < 11
$$

Divide by 4:
$$
-\frac{1}{4} < x < \frac{11}{4}
$$

So the solution is $ -\frac{1}{4} < x < \frac{11}{4} $

But since no options are shown for this question (only A-D), and it’s likely multiple choice, but we don’t have the choices listed — so I’ll stop here unless you provide them.

But based on the pattern, perhaps the answer format is missing.

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Summary of Answers:

| Question | Answer |
|--------|--------|
| 1 | B → $ x = -\frac{7}{3}, -1 $ |
| 2 | A → $ -4 < x < 4 $ |
| 3 | B → $ \frac{4}{3} < x < 2 $ |
| 4 | C → $ x = -5, -1 $ |
| 5 | C → $ x = \frac{2}{3}, 1 $ |
| 6 | A → $ x = 1 $ |
| 7 | $ -\frac{1}{4} < x < \frac{11}{4} $ (No options given) |

Let me know if you want help with questions 8–10 or need explanations for any part!