6
algebra

Solve: 6x>26 - x > 2

A

x<4x < 4

B

x>4x > 4

C

x<8x < 8

D

x>8x > 8

Correct Answer: A

Choice A is the correct answer. When a variable term is subtracted, we need to carefully handle the negation.

  1. Subtract 6: 6x6>266 - x - 6 > 2 - 6, giving x>4-x > -4
  2. Divide by -1: x1<41\frac{-x}{-1} < \frac{-4}{-1} (REVERSE the sign!)
  3. Simplify: x<4x < 4

?�� Strategic Tip: Dividing by -1 (or multiplying by -1) reverses the inequality. Alternatively, you can add xx to both sides first: 6>2+x6 > 2 + x, then solve.

Choice B is incorrect because it fails to reverse the inequality when dividing by -1. Choice C is incorrect because it adds 6 and 2 to get 8, using faulty arithmetic. Choice D is incorrect because it combines both wrong value and wrong direction.