Set 8: Linear Inequalities (Intermediate)

Choice A is correct. Choice A is the correct answer. Distribution and multi-step solving are combined in this problem. 1. Distribute: $2(3 x) - 2(4) \geq 5 x + 2$, giving $6x - 8 \geq 5 x + 2$ 2. Subtract 5 x: $6x - 5 x - 8 \geq 5 x - 5 x + 2$, giving $x - 8 \geq 2$ 3. Add 8: $x \geq 10$ Strategic Tip: When distributing with parentheses, multiply the coefficient by EVERY term inside. Choice B is incorrect because it reverses the inequality without justification. Choice C is incorrect because it uses -10 instead of 10, possibly from a sign error. Choice D is incorrect because it combines both wrong sign and wrong direction.