8
algebra

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

A

x1x \geq 1

B

1x31 \leq x \leq 3

C

x3x \geq -3

D

3x1-3 \leq x \leq 1

Correct Answer: A

Choice A is the correct answer. Intersection of sets.

  1. First: 62x42x2x16 - 2x \leq 4 \rightarrow -2x \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.