Set 8: Linear Inequalities

Choice A is correct. Choice A is the correct answer. When a variable term is subtracted, we need to carefully handle the negation. 1. Subtract 6: $6- x - 6 > 2 - 6$, giving $-x > -4$ 2. Divide by -1: $\frac{-x}{-1} < \frac{-4}{-1}$ (REVERSE the sign!) 3. Simplify: $x < 4$ Strategic Tip: Dividing by -1 (or multiplying by -1) reverses the inequality. Alternatively, you can add $x$ to both sides first: $6> 2 + x$, then solve. Choice B is incorrect because it fails to reverse the inequality when dividing by -1. Choice C is incorrect because it adds 6 and 2 to get 8, using faulty arithmetic. Choice D is incorrect because it combines both wrong value and wrong direction.