4
algebra

Solve: 2x34x+131\frac{2x - 3}{4} - \frac{x + 1}{3} \geq 1

A

x12.5x \geq 12.5

B

x12.5x \leq 12.5

C

x10x \geq 10

D

x1x \geq 1

Correct Answer: A

Choice A is the correct answer. Clear fractions with LCD = 12.

  1. Multiply by 12: 3(2x3)4(x+1)12(1)3(2x - 3) - 4(x + 1) \geq 12(1)
  2. Distribute: 6x94x4126x - 9 - 4x - 4 \geq 12
  3. Combine: 2x13122x - 13 \geq 12
  4. Add 13: 2x252x \geq 25
  5. Divide by 2: x12.5x \geq 12.5

?�� Strategic Tip: Don't forget to distribute the negative sign to the second term: 4(1)=4-4(1) = -4.

Choice B is incorrect because it reverses the inequality. Choice C is incorrect because it solves incorrectly. Choice D is incorrect because it solves incorrectly.