6
algebra

Solve: 2x+1>6-2|x + 1| > -6

A

4<x<2-4 < x < 2

B

x>2x > 2 or x<4x < -4

C

2<x<4-2 < x < 4

D

No solution

Correct Answer: A

Choice A is the correct answer. Isolate the absolute value first.

  1. Divide by -2: x+1<3|x + 1| < 3 (Reverse sign!)
  2. Setup: 3<x+1<3-3 < x + 1 < 3
  3. Subtract 1: 4<x<2-4 < x < 2

?�� Strategic Tip: Always isolate ...|...| before splitting. Dividing by a negative flips >> to <<.

Choice B is incorrect because it forgets to flip the inequality sign when dividing by -2. Choice C is incorrect because it solves incorrectly. Choice D is incorrect because it assumes absolute value can't be greater than a negative (but we divided by negative first).