2
algebra

Solve: 7x43x+127x - 4 \geq 3x + 12

A

x4x \geq 4

B

x4x \leq 4

C

x2x \geq 2

D

x2x \leq 2

Correct Answer: A

Choice A is the correct answer. Variables on both sides require systematic isolation.

  1. Subtract 3x: 7x3x43x3x+127x - 3x - 4 \geq 3x - 3x + 12, giving 4x4124x - 4 \geq 12
  2. Add 4: 4x4+412+44x - 4 + 4 \geq 12 + 4, giving 4x164x \geq 16
  3. Divide by 4: x4x \geq 4

?�� Strategic Tip: Move all variable terms to one side before working with constants to avoid confusion.

Choice B is incorrect because it reverses the inequality without mathematical reason. Choice C is incorrect because it might result from incorrect arithmetic, perhaps dividing 8 by 4 instead of 16. Choice D is incorrect because it combines both wrong value and wrong direction.