Set 11: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. Distributing negative coefficients requires careful sign tracking. 1. Distribute: $-2(3 x) - 2(-4) \leq 10$, giving $-6 x + 8 \leq 10$ 2. Subtract 8: $-6 x \leq 2$ 3. Divide by -6: $x \geq -\frac{2}{6} = -\frac{1}{3}$ (REVERSE!) Strategic Tip: When distributing a negative, every term inside changes sign. Then dividing by negative reverses the inequality. Choice B is incorrect because it fails to reverse the inequality when dividing by -6. Choice C is incorrect because it has the wrong sign on the fraction (should be negative). Choice D is incorrect because it combines wrong sign and wrong direction.