5
algebra

If 2x53x3\frac{2x - 5}{3} \geq x - 3, what is the solution?

A

x4x \leq 4

B

x4x \geq 4

C

x2x \leq 2

D

x2x \geq 2

Correct Answer: A

Choice A is the correct answer. Multiply by the denominator to clear the fraction.

  1. Multiply by 3: 2x53(x3)2x - 5 \geq 3(x - 3)
  2. Distribute: 2x53x92x - 5 \geq 3x - 9
  3. Subtract 2x: 5x9-5 \geq x - 9
  4. Add 9: 4x4 \geq x, or x4x \leq 4

?�� Strategic Tip: Don't forget to multiply the entire right side (x3)(x-3) by 3.

Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it might result from arithmetic errors. Choice D is incorrect because it combines wrong value and wrong direction.