Set 7: Linear Inequalities

Choice A is correct. 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: $12(\frac{x}{3}) - 12(2) < 12(\frac{x}{4}) + 12(1)$ 3. Simplify: $4x - 24 < 3 x + 12$ 4. Subtract 3 x: $x - 24 < 12$ 5. Add 24: $x < 36$ 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.