8
algebra

Which value is a solution to 4(2x)3(x4)+64(2 - x) \leq 3(x - 4) + 6?

A

x=2x = 2

B

x=1x = 1

C

x=0x = 0

D

x=1x = -1

Correct Answer: A

Choice A is the correct answer. Solve the inequality first.

  1. Distribute: 84x3x12+68 - 4x \leq 3x - 12 + 6
  2. Simplify: 84x3x68 - 4x \leq 3x - 6
  3. Add 4x: 87x68 \leq 7x - 6
  4. Add 6: 147x14 \leq 7x
  5. Divide by 7: 2x2 \leq x, or x2x \geq 2
  6. Test Choices: We need a value 2\geq 2. Only x=2x=2 works (boundary value).

?�� Strategic Tip:x2x \geq 2 means 2 is included.

Choice B is incorrect because 1 is not 2\geq 2. Choice C is incorrect because 0 is not 2\geq 2. Choice D is incorrect because -1 is not 2\geq 2.