Set 17: Linear Inequalities

Explanation

Answer: A

Solve: $|3x - 2| \leq 7$

$-\frac{5}{3} \leq x \leq 3$

✓ Correct

$-3 \leq x \leq 3$

$x \leq 3$

$x \leq -\frac{5}{3}$ or $x \geq 3$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. "Less thAND" $\rightarrow$ Compound inequality. 1. Setup: $-7 \leq 3 x - 2 \leq 7$ 2. Add 2: $-5 \leq 3 x \leq 9$ 3. Divide by 3: $-\frac{5}{3} \leq x \leq 3$ Strategic Tip: Add the constant to both sides of the compound inequality. Choice B is incorrect because it solves the left side incorrectly. Choice C is incorrect because it misses the lower bound. Choice D is incorrect because it treats it as an "or" inequality.

Key Steps:

•

The correct answer is $-\frac{5}{3} \leq x \leq 3$

Why others are wrong:

B: Choice B is incorrect and may result from a calculation error.

C: Choice C is incorrect and may result from a calculation error.

D: Choice D is incorrect and may result from a calculation error.

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