5
algebra

Solve: 52x15 - 2x \geq 1

A

x2x \geq 2

B

x2x \leq 2

C

x3x \geq 3

D

x3x \leq 3

Correct Answer: B

Choice B is the correct answer. When the variable term is negative, we must eventually divide by a negative number.

  1. Subtract 5: 52x5155 - 2x - 5 \geq 1 - 5, giving 2x4-2x \geq -4
  2. Divide by -2: 2x242\frac{-2x}{-2} \leq \frac{-4}{-2} (reverse the sign!)
  3. Simplify: x2x \leq 2

?�� Strategic Tip: ALWAYS reverse the inequality when multiplying or dividing by negative numbers. This is one of the most tested concepts on the SAT.

Choice A is incorrect because it fails to reverse the inequality sign when dividing by -2. Choice C is incorrect because it appears to use incorrect arithmetic, possibly dividing -6 by -2. Choice D is incorrect because while it correctly reverses the sign, it uses the wrong boundary value (3 instead of 2).