8
algebra

Solve: 4(x+2)>2(x8)-4(x + 2) > 2(x - 8)

A

x<43x < \frac{4}{3}

B

x>43x > \frac{4}{3}

C

x<4x < 4

D

x>4x > 4

Correct Answer: A

Choice A is the correct answer. Distribute and collect terms.

  1. Distribute: 4x8>2x16-4x - 8 > 2x - 16
  2. Add 4x: 8>6x16-8 > 6x - 16
  3. Add 16: 8>6x8 > 6x
  4. Divide by 6: 86>x\frac{8}{6} > x, which simplifies to 43>x\frac{4}{3} > x or x<43x < \frac{4}{3}

?�� Strategic Tip: Be careful with signs when distributing negatives. 4(2)=8-4(2) = -8.

Choice B is incorrect because it reverses the inequality direction (should be x<x <). Choice C is incorrect because it might result from arithmetic errors like 6x<246x < 24. Choice D is incorrect because it combines wrong value and wrong direction.