Set 14: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. This two-step inequality requires both subtraction and division. 1. Subtract 5: $2x + 5 - 5 > 13 - 5$, giving $2x > 8$ 2. Divide by 2: $\frac{2 x}{2} > \frac{8}{2}$, giving $x > 4$ 3. Verify: Try $x = 5$: $2(5) + 5 = 15 > 13$ Strategic Tip: Two-step inequalities follow the same order as two-step equations: first eliminate the constant, then eliminate the coefficient. Choice B is incorrect because it reverses the inequality direction without justification (we divided by positive 2, which doesn't reverse the sign). Choice C is incorrect because it adds 5 and 13 to get 18, then halves it, using faulty logic. Choice D is incorrect because it combines the wrong value (9) with the wrong direction (<).