2
algebra

Which is the solution to 3(x+2)12-3(x + 2) \geq 12?

A

x6x \leq -6

B

x6x \geq -6

C

x2x \leq -2

D

x2x \geq -2

Correct Answer: A

Choice A is the correct answer. Distributing a negative coefficient creates a negative variable term.

  1. Distribute: 3(x)+(3)(2)12-3(x) + (-3)(2) \geq 12, giving 3x612-3x - 6 \geq 12
  2. Add 6: 3x18-3x \geq 18
  3. Divide by -3: x6x \leq -6 (REVERSE the sign!)

?�� Strategic Tip: When dividing by a negative number, always flip the inequality direction.

Choice B is incorrect because it fails to reverse the inequality when dividing by -3. Choice C is incorrect because it uses -2 instead of -6, possibly from incorrect arithmetic. Choice D is incorrect because it combines the wrong value with failure to reverse the sign.