Set 7: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. Fractions in inequalities can be eliminated by multiplying both sides by the denominator. 1. Multiply by 3: $3\cdot \frac{2 x - 6}{3} \geq 3 \cdot 4$, giving $2x - 6 \geq 12$ 2. Add 6: $2x - 6 + 6 \geq 12 + 6$, giving $2x \geq 18$ 3. Divide by 2: $x \geq 9$ Strategic Tip: Multiplying by a positive denominator clears fractions without changing the inequality direction. Choice B is incorrect because it reverses the inequality sign without cause. Choice C is incorrect because it might result from dividing 6 by 2 instead of properly solving the multi-step inequality. Choice D is incorrect because it uses incorrect arithmetic, possibly (12+6)/2 = 9, then subtracting 2.