Set 5: Linear Inequalities (Advanced)

Choice A is correct. Choice A is the correct answer. Be careful multiplying by $x$ (sign change if negative). 1. Case 1 ($x > 0$): Multiply by $x$: $1> 2 x \rightarrow 0.5 > x$. Combined with $x>0$: $0< x < 0.5$. 2. Case 2 ($x < 0$): Multiply by $x$ (reverse sign): $1< 2 x \rightarrow 0.5 < x$. But $x$ must be negative, so no solution here ($0.5< x < 0$ is impossible). 3. Result: $0< x < 0.5$ Strategic Tip: For rational inequalities, consider the sign of the denominator. Or test points: $x=0.1 \rightarrow 10 > 2$ (True). $x=1 \rightarrow 1 > 2$ (False). Choice B is incorrect. Choice C is incorrect because it includes negative numbers. Choice D is incorrect.