8
algebra

Solve: 4(2x3)5(x+1)4(2x - 3) \geq 5(x + 1)

A

x173x \geq \frac{17}{3}

B

x173x \leq \frac{17}{3}

C

x7x \geq 7

D

x7x \leq 7

Correct Answer: A

Choice A is the correct answer. Distribute both sides, then collect like terms.

  1. Distribute left: 8x125x+58x - 12 \geq 5x + 5
  2. Subtract 5x: 3x1253x - 12 \geq 5
  3. Add 12: 3x173x \geq 17
  4. Divide by 3: x173x \geq \frac{17}{3}

?�� Strategic Tip: When both sides have parentheses, distribute each side completely before combining.

Choice B is incorrect because it reverses the inequality without justification. Choice C is incorrect because it uses 7 instead of 1735.67\frac{17}{3} \approx 5.67. Choice D is incorrect because it combines wrong value and wrong direction.