Set 6: Linear Inequalities (Advanced)

Choice A is correct. Choice A is the correct answer. Split into cases. 1. Case 1: $2x - 5 > 3 x \rightarrow -5 > x \rightarrow x < -5$ 2. Case 2: $2x - 5 < -3 x \rightarrow 5 x < 5 \rightarrow x < 1$ 3. Combine: The union of $x < -5$ and $x < 1$ is $x < 1$ (since $x<-5$ is inside $x<1$). - Check $x=0$: $|-5| > 0$ (5>0) True. - Check $x=-6$: $|-17| > -18$ (17>-18) True. - Check $x=2$: $|-1| > 6$ (1>6) False. $|A| > B$ is $A > B$ or $A < -B$. 1. $2x - 5 > 3 x \rightarrow -x > 5 \rightarrow x < -5$ 2. $2x - 5 < -3 x \rightarrow 5 x < 5 \rightarrow x < 1$ Union: $x < 1$ OR $x < -5$. The set $x < 1$ includes $x < -5$. So $x < 1$. So $x < 1$ seems correct. Choice A is correct. Choice B is incorrect (subset). Choice C is incorrect. Choice D is incorrect.