Set 4: Linear Inequalities

Choice B is correct. Choice B is the correct answer. Negative coefficients require sign reversal when dividing. 1. Subtract 10: $-5 x + 10 - 10 \leq 30 - 10$, giving $-5 x \leq 20$ 2. Divide by -5: $\frac{-5 x}{-5} \geq \frac{20}{-5}$ (REVERSE the sign!) 3. Simplify: $x \geq -4$ Strategic Tip: Dividing by -5 changes $\leq$ to $\geq$. This reversal is critical and heavily tested. Choice A is incorrect because it fails to reverse the inequality sign when dividing by -5. Choice C is incorrect because it might come from dividing 40 by 5, using wrong intermediate calculations. Choice D is incorrect because while it correctly reverses the sign, it uses the wrong boundary value.