Set 2: Linear Inequalities

Choice C is correct. Choice C is the correct answer. Solve and interpret the union. 1. First: $4x - 4 < 8 \rightarrow 4 x < 12 \rightarrow x < 3$ 2. Second: $2x + 6 > 12 \rightarrow 2 x > 6 \rightarrow x > 3$ 3. Combine: $x < 3$ or $x > 3$ 4. Interpretation: This includes every number EXCEPT 3. So $x \neq 3$. Strategic Tip: If the arrows point away from a single hole, the solution is "all real numbers except [hole]". Choice A is incorrect because while technically true, $x \neq 3$ is the standard concise form. Choice B is incorrect because it solves the second part incorrectly. Choice D is incorrect because it includes 3, which is not a solution.