Question

solve the inequality for x.

$-6 \leq -8 + \frac{x}{6}$

simplify your answer as much as possible.

Explanation:

Step1: Add 8 to both sides

To isolate the term with \( x \), we add 8 to both sides of the inequality \(-6 \leq -8 + \frac{x}{6}\).

$$ -6 + 8 \leq -8 + 8 + \frac{x}{6} $$

Simplifying the left and right sides, we get:

$$ 2 \leq \frac{x}{6} $$

Step2: Multiply both sides by 6

To solve for \( x \), we multiply both sides of the inequality \( 2 \leq \frac{x}{6} \) by 6.

$$ 2 \times 6 \leq \frac{x}{6} \times 6 $$

Simplifying both sides, we obtain:

$$ 12 \leq x $$

Which can be rewritten as \( x \geq 12 \).

Answer:

\( x \geq 12 \)