4
algebra

Solve: 4(x1)<84(x - 1) < 8 or 2(x+3)>122(x + 3) > 12

A

x<3x < 3 or x>3x > 3

B

x<3x < 3 or x>6x > 6

C

xeq3x eq 3

D

All real numbers

Correct Answer: C

Choice C is the correct answer. Solve and interpret the union.

  1. First: 4x4<84x<12x<34x - 4 < 8 \rightarrow 4x < 12 \rightarrow x < 3
  2. Second: 2x+6>122x>6x>32x + 6 > 12 \rightarrow 2x > 6 \rightarrow x > 3
  3. Combine: x<3x < 3 or x>3x > 3
  4. Interpretation: This includes every number EXCEPT 3. So xeq3x eq 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, xeq3x eq 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.