3
algebra

Solve: 2x+512x + 5 \geq 1 and 3x>12-3x > -12

A

2x<4-2 \leq x < 4

B

2x<6-2 \leq x < 6

C

x2x \geq -2

D

x<4x < 4

Correct Answer: A

Choice A is the correct answer. Solve independently and find the intersection.

  1. First: 2x4x22x \geq -4 \rightarrow x \geq -2
  2. Second: 3x>12x<4-3x > -12 \rightarrow x < 4 (Reverse sign!)
  3. Combine: x2x \geq -2 AND x<42x<4x < 4 \rightarrow -2 \leq x < 4

?�� Strategic Tip: Don't forget to reverse the sign when dividing by -3.

Choice B is incorrect because it might result from dividing 12 by 2 instead of 3. Choice C is incorrect because it ignores the second constraint. Choice D is incorrect because it ignores the first constraint.