4
algebra

Solve: x32<x4+1\frac{x}{3} - 2 < \frac{x}{4} + 1

A

x<36x < 36

B

x>36x > 36

C

x<12x < 12

D

x>12x > 12

Correct Answer: A

Choice A is the correct answer. Eliminate fractions by multiplying by the Least Common Multiple (LCM) of the denominators.

  1. LCM of 3 and 4 is 12: Multiply every term by 12.
  2. Multiply: 12(x3)12(2)<12(x4)+12(1)12(\frac{x}{3}) - 12(2) < 12(\frac{x}{4}) + 12(1)
  3. Simplify: 4x24<3x+124x - 24 < 3x + 12
  4. Subtract 3x: x24<12x - 24 < 12
  5. Add 24: x<36x < 36

?�� Strategic Tip: Clearing fractions early reduces calculation errors. Multiply EVERY term, including constants.

Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it might come from not multiplying the constants by 12. Choice D is incorrect because it combines wrong value and wrong direction.