2
algebra

Solve: x3<5|x - 3| < 5

A

2<x<8-2 < x < 8

B

x<8x < 8

C

x<2x < -2 or x>8x > 8

D

8<x<2-8 < x < 2

Correct Answer: A

Choice A is the correct answer. Absolute value inequalities with << become compound "and" inequalities.

  1. Setup: 5<x3<5-5 < x - 3 < 5
  2. Add 3: 5+3<x<5+3-5 + 3 < x < 5 + 3
  3. Simplify: 2<x<8-2 < x < 8

?�� Strategic Tip:A<b|A| < b becomes b<A<b-b < A < b. Think "Less thAND" (Less than = And).

Choice B is incorrect because it ignores the lower bound. Choice C is incorrect because it models x3>5|x-3| > 5 ("GreatOR" = Or). Choice D is incorrect because it solves incorrectly.