Set 2: Linear Inequalities (Advanced)

Explanation

Answer: A

Solve: $2|x - 1| + 3 \leq 9$

$-2 \leq x \leq 4$

✓ Correct

$-4 \leq x \leq 2$

$x \leq 4$

$x \leq -2$ or $x \geq 4$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Isolate and solve. 1. Subtract 3: $2|x - 1| \leq 6$ 2. Divide by 2: $|x - 1| \leq 3$ 3. Compound: $-3 \leq x - 1 \leq 3$ 4. Add 1: $-2 \leq x \leq 4$ Strategic Tip: Treat $|...|$ as a variable until it is isolated. Choice B is incorrect because it solves 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 $-2 \leq x \leq 4$

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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