2
algebra

What is the solution to 3x7113x - 7 \leq 11?

A

x6x \leq 6

B

x6x \geq 6

C

x43x \leq \frac{4}{3}

D

x18x \leq 18

Correct Answer: A

Choice A is the correct answer. Solving two-step inequalities systematically prevents errors.

  1. Add 7: 3x7+711+73x - 7 + 7 \leq 11 + 7, giving 3x183x \leq 18
  2. Divide by 3: 3x3183\frac{3x}{3} \leq \frac{18}{3}, giving x6x \leq 6
  3. Interpretation: All values up to and including 6 satisfy this inequality

?�� Strategic Tip: Always perform inverse operations in the correct order: handle addition/subtraction before multiplication/division.

Choice B is incorrect because it reverses the inequality sign without mathematical justification. Choice C is incorrect because it appears to subtract 7 from 11 to get 4, then divide by 3, skipping proper steps. Choice D is incorrect because it shows only the intermediate step 3x183x \leq 18 without dividing by 3.