Set 8: Linear Inequalities

Choice B is correct. Choice B is the correct answer. Some inequalities lead to contradictions when simplified. 1. Simplify: Subtract $2x$ from both sides: $2x - 2 x + 1 < 2 x - 2 x - 4$ 2. Result: $1< -4$ 3. Contradiction: This is FALSE, so no value of $x$ satisfies this inequality Strategic Tip: When variables cancel and you're left with a false statement (like $1< -4$), the inequality has no solution. Choice A is incorrect because subtracting $x$ gives $5> 3$, which is ALWAYS true (all real numbers are solutions). Choice C is incorrect because this simplifies to $0\geq 0$, which is true, so all real numbers work. Choice D is incorrect because subtracting $x$ gives $-2 \leq 1$, always true.