Set 7: Linear Inequalities

Choice A is correct. Choice A is the correct answer. Solving inequalities with negative coefficients requires reversing the inequality sign. 1. Subtract 5: $5- 2 x - 5 \geq 17 - 5$, giving $-2 x \geq 12$ 2. Divide by -2: $\frac{-2 x}{-2} \leq \frac{12}{-2}$ (REVERSE the sign!) 3. Simplify: $x \leq -6$ Strategic Tip: Dividing by a negative number is the most common trap in linear inequalities. Always check the sign direction. Choice B is incorrect because it fails to reverse the inequality sign when dividing by -2. Choice C is incorrect because it uses positive 6 instead of negative 6. Choice D is incorrect because it combines wrong sign and wrong direction.