Question

solve the following inequality
\\(\frac{3x + 2}{7} - \frac{3x - 1}{10} \leq -4\\)

select the correct choice and fill in the answer box to complete your choice.
\\(\bigcirc\\) a. \\(x < \square\\)
\\(\bigcirc\\) b. \\(x \leq \square\\)
\\(\bigcirc\\) c. \\(x > \square\\)
\\(\bigcirc\\) d. \\(x \geq \square\\)

Explanation:

Step1: Eliminate denominators

Multiply all terms by 70 (LCM of 7 and 10):
$$10(3x+2) - 7(3x-1) \leq -4 \times 70$$

Step2: Expand brackets

Calculate each expanded term:
$$30x + 20 - 21x + 7 \leq -280$$

Step3: Combine like terms

Simplify left-hand side:
$$9x + 27 \leq -280$$

Step4: Isolate variable term

Subtract 27 from both sides:
$$9x \leq -280 - 27$$
$$9x \leq -307$$

Step5: Solve for x

Divide by 9 on both sides:
$$x \leq \frac{-307}{9}$$
$$x \leq -34\frac{1}{9}$$

Answer:

B. $x \leq -\frac{307}{9}$