Set 1: Linear Inequalities

Choice B is correct. Choice B is the correct answer. Identify where the inequality rule was violated. 1. Step 1 Check: Subtract 3 from both sides. $3- 2 x - 3 \leq 11 - 3 \rightarrow -2 x \leq 8$. This is correct. 2. Step 2 Check: Divide by -2. $\frac{-2 x}{-2} \leq \frac{8}{-2}$. Since we divided by a negative, the sign MUST reverse. It should be $x \geq -4$. The step shows $x \leq -4$, which is incorrect. Strategic Tip: Always double-check the inequality direction when multiplying or dividing by a negative number. Choice A is incorrect because Step 1 correctly subtracts 3. Choice C is incorrect because Step 3 is just interpreting Step 2, so the root error is in Step 2. Choice D is incorrect because the sign was not reversed in Step 2.