4
algebra

Solve: 5<32x9-5 < 3 - 2x \leq 9

A

3x<4-3 \leq x < 4

B

3<x4-3 < x \leq 4

C

4x<3-4 \leq x < 3

D

4<x34 < x \leq -3

Correct Answer: A

Choice A is the correct answer. Isolate xx and reverse signs.

  1. Subtract 3: 8<2x6-8 < -2x \leq 6
  2. Divide by -2: 4>x34 > x \geq -3 (Reverse signs!)
  3. Rewrite: 3x<4-3 \leq x < 4

?�� Strategic Tip: When rewriting 4>x34 > x \geq -3, start with the smallest number: 3x<4-3 \leq x < 4.

Choice B is incorrect because it swaps the strict/inclusive endpoints. Choice C is incorrect because it calculates endpoints incorrectly. Choice D is incorrect because it writes the interval backwards (4<34 < -3 is impossible).