8
algebra

Which inequality is equivalent to 2x3>4x+52x - 3 > 4x + 5?

A

2x>8-2x > 8

B

2x<8-2x < 8

C

2x>82x > 8

D

x>4x > -4

Correct Answer: A

Choice A is the correct answer. Finding equivalent forms helps verify solutions.

  1. Subtract 4x: 2x4x3>4x4x+52x - 4x - 3 > 4x - 4x + 5, giving 2x3>5-2x - 3 > 5
  2. Add 3: 2x>8-2x > 8 ??n3. Continue to solve: Divide by -2: x<4x < -4

?�� Strategic Tip: Equivalent inequalities have the same solution set but may look different in form.

Choice B is incorrect because it has the opposite direction for 2x-2x. Choice C is incorrect because it has the wrong sign on the coefficient (should be 2x-2x, not 2x2x). Choice D is incorrect because while this represents the final solution when fully solved, it's not equivalent to the intermediate form requested, and the direction should be <<, not >>.