8
algebra

Solve: 2x+19|2x + 1| \geq 9

A

x4x \geq 4 or x5x \leq -5

B

5x4-5 \leq x \leq 4

C

x4x \geq 4

D

x5x \leq -5

Correct Answer: A

Choice A is the correct answer. Absolute value \geq splits into two "or" inequalities.

  1. Case 1: 2x+192x8x42x + 1 \geq 9 \rightarrow 2x \geq 8 \rightarrow x \geq 4
  2. Case 2: 2x+192x10x52x + 1 \leq -9 \rightarrow 2x \leq -10 \rightarrow x \leq -5
  3. Combine: x4x \geq 4 or x5x \leq -5

?�� Strategic Tip: "GreatOR" = Or. Split into positive and negative cases, flipping the sign for the negative case.

Choice B is incorrect because it models 2x+19|2x+1| \leq 9 ("Less thAND"). Choice C is incorrect because it misses the negative case. Choice D is incorrect because it misses the positive case.