1
algebra

Solve: 3(2x5)+4253(2x - 5) + 4 \leq 25

A

x4x \leq 4

B

x4x \geq 4

C

x6x \leq 6

D

x6x \geq 6

Correct Answer: A

Choice A is the correct answer. Multi-step inequalities with distribution require careful order of operations.

  1. Distribute: 3(2x)3(5)+4253(2x) - 3(5) + 4 \leq 25, giving 6x15+4256x - 15 + 4 \leq 25
  2. Combine like terms: 6x11256x - 11 \leq 25
  3. Add 11: 6x366x \leq 36
  4. Divide by 6: x4x \leq 4

?�� Strategic Tip: When distributing, multiply the coefficient by each term inside the parentheses, then combine like terms before isolating the variable.

Choice B is incorrect because it reverses the inequality without justification (we divided by positive 6). Choice C is incorrect because it might result from incorrectly combining -15 and 4 to get -11, then adding to 25 incorrectly. Choice D is incorrect because it combines both wrong value and wrong direction.