Set 13: Linear Inequalities (Advanced)

Choice A is correct. Choice A is the correct answer. Solve the compound inequality by performing operations on all three parts simultaneously. 1. Subtract 1: $-3 - 1 < 2 x + 1 - 1 \leq 7 - 1$, giving $-4 < 2 x \leq 6$ 2. Divide by 2: $\frac{-4}{2} < \frac{2 x}{2} \leq \frac{6}{2}$ 3. Simplify: $-2 < x \leq 3$ Strategic Tip: Whatever you do to the middle, you must do to the left and right sides. Choice B is incorrect because it swaps the strict ($<$) and inclusive ($\leq$) inequalities. Choice C is incorrect because it might result from adding 1 instead of subtracting. Choice D is incorrect because it combines wrong values and wrong signs.