8
algebra

Which value satisfies 2(x+3)>10-2(x + 3) > -10?

A

x=3x = 3

B

x=2x = 2

C

x=1x = 1

D

x=5x = 5

Correct Answer: C

Choice C is the correct answer. Solve the inequality first to find the valid range.

  1. Distribute: 2x6>10-2x - 6 > -10
  2. Add 6: 2x>4-2x > -4
  3. Divide by -2: x<2x < 2 (REVERSE the sign!)
  4. Test: Only x=1x = 1 satisfies x<2x < 2
  5. Verify: 2(1+3)=2(4)=8>10-2(1+3) = -2(4) = -8 > -10 ??n ?�� Strategic Tip: When distributing a negative, remember that 2(x+3)=2x6-2(x+3) = -2x - 6, not 2x+6-2x + 6.

Choice A is incorrect becausex=3x = 3 does not satisfy x<2x < 2 (3 is greater than 2). Choice B is incorrect becausex=2x = 2 is the boundary and doesn't satisfy the strict inequality x<2x < 2. Choice D is incorrect becausex=5x = 5 is well outside the solution range x<2x < 2.