Set 16: Linear Inequalities (Intermediate)

Choice C is correct. Choice C is the correct answer. Solve the inequality first to find the valid range. 1. Distribute: $-2 x - 6 > -10$ 2. Add 6: $-2 x > -4$ 3. Divide by -2: $x < 2$ (REVERSE the sign!) 4. Test: Only $x = 1$ satisfies $x < 2$ 5. Verify: $-2(1+3) = -2(4) = -8 > -10$ Strategic Tip: When distributing a negative, remember that $-2(x+3) = -2 x - 6$, not $-2 x + 6$. Choice A is incorrect because $x = 3$ does not satisfy $x < 2$ (3 is greater than 2). Choice B is incorrect because $x = 2$ is the boundary and doesn't satisfy the strict inequality $x < 2$. Choice D is incorrect because $x = 5$ is well outside the solution range $x < 2$.