Set 15: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. Use the LCD to clear fractions. 1. LCD of 3 and 2 is 6: Multiply all terms by 6. 2. Multiply: $6(\frac{2}{3}x) + 6(5) > 6(\frac{1}{2}x) + 6(6)$ 3. Simplify: $4x + 30 > 3 x + 36$ 4. Subtract 3 x: $x + 30 > 36$ 5. Subtract 30: $x > 6$ Strategic Tip: Clearing fractions makes the algebra much simpler and less prone to arithmetic errors. Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it might result from not multiplying the constants by 6. Choice D is incorrect because it combines wrong value and wrong direction.