1
algebra

Solve: 2(4x)>3x+182(4 - x) > 3x + 18

A

x<2x < -2

B

x>2x > -2

C

x<2x < 2

D

x>2x > 2

Correct Answer: A

Choice A is the correct answer. Distribute and isolate the variable.

  1. Distribute: 82x>3x+188 - 2x > 3x + 18
  2. Add 2x: 8>5x+188 > 5x + 18
  3. Subtract 18: 10>5x-10 > 5x
  4. Divide by 5: 2>x-2 > x, which is equivalent to x<2x < -2

?�� Strategic Tip: Keeping the variable positive (by adding 2x2x) avoids dividing by a negative, but you must read the inequality correctly from the variable's perspective (2>x-2 > x means xx is less than 2-2).

Choice B is incorrect because it reverses the inequality direction. Choice C is incorrect because it uses positive 2 instead of negative 2. Choice D is incorrect because it combines wrong value and wrong direction.