9

Set 4: Linear Inequalities (Intermediate)

Explanation

Answer: A

Solve: 102x46-10 \leq 2x - 4 \leq 6

A.

3x5-3 \leq x \leq 5

✓ Correct
B.

3x1-3 \leq x \leq 1

C.

7x5-7 \leq x \leq 5

D.

7x1-7 \leq x \leq 1

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Isolate xx in the middle. 1. Add 4: 10+42x6+4-10 + 4 \leq 2 x \leq 6 + 4, giving 62x10-6 \leq 2 x \leq 10 2. Divide by 2: 3x5-3 \leq x \leq 5 Strategic Tip: Check both endpoints: 6/2=3-6/2 = -3 and 10/2=510 /2 = 5. Choice B is incorrect because it divides 6 by 2 incorrectly or forgets to add 4 to the right side. Choice C is incorrect because it subtracts 4 instead of adding. Choice D is incorrect because it combines multiple errors.

Key Steps:

The correct answer is 3x5-3 \leq x \leq 5

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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