6

Set 16: Linear Inequalities

Explanation

Answer: A

Solve: 2(3x)42(3 - x) \leq 4 and x+52x + 5 \geq 2

A.

x1x \geq 1

✓ Correct
B.

1x31 \leq x \leq 3

C.

x3x \geq -3

D.

3x1-3 \leq x \leq 1

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Intersection of sets. 1. First: 62x42x2x16- 2 x \leq 4 \rightarrow -2 x \leq -2 \rightarrow x \geq 1 2. Second: x3x \geq -3 3. Combine: x1x \geq 1 AND x3x \geq -3. The intersection is x1x \geq 1 (since 1 is greater than -3). Strategic Tip: If both are "greater than", the intersection is "greater than the larger number". Choice B is incorrect. Choice C is incorrect because it is the union, not intersection. Choice D is incorrect.

Key Steps:

The correct answer is x1x \geq 1

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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