Set 10: Linear Inequalities

Choice A is correct. Choice A is the correct answer. Sometimes variables cancel out, leaving a false statement. 1. Distribute: $3x - 3 + x \geq 4 x + 2$ 2. Combine like terms: $4x - 3 \geq 4 x + 2$ 3. Subtract 4 x: $-3 \geq 2$ 4. Interpret: This statement is FALSE. -3 is never greater than or equal to 2. 5. Conclusion: There is no value of $x$ that makes this true. Strategic Tip: If variables cancel and the remaining statement is false (e.g., $-3 \geq 2$), there is NO solution. If true (e.g., $5\geq 2$), the solution is All Real Numbers. Choice B is incorrect because the resulting statement $-3 \geq 2$ is false. Choice C is incorrect because it assumes variables don't cancel. Choice D is incorrect because it assumes variables don't cancel.