Set 14: Linear Inequalities

Choice A is correct. Choice A is the correct answer. Combining like terms after distribution simplifies the inequality. 1. Distribute: $5x - 2 x + 6 < 18$ (note: $-2(x-3) = -2 x + 6$) 2. Combine like terms: $3x + 6 < 18$ 3. Subtract 6: $3x < 12$ 4. Divide by 3: $x < 4$ Strategic Tip: When distributing $-2(x-3)$, remember both terms get multiplied: $-2 x$ and $-2(-3) = +6$. Choice B is incorrect because it reverses the inequality without mathematical reason. Choice C is incorrect because it might skip combining like terms properly (5 x - 2 x). Choice D is incorrect because it combines wrong value and wrong direction.