Solve the Inequality for x -2<=(3x-1)/8<=0

$- 2 \leq \frac{3 x - 1}{8} \leq 0$

Multiply each term in the inequality by $8$ .

$- 2 \cdot 8 \leq \frac{3 x - 1}{8} \cdot 8 \leq 0 \cdot 8$

Multiply $- 2$ by $8$ .

$- 16 \leq \frac{3 x - 1}{8} \cdot 8 \leq 0 \cdot 8$

Cancel the common factor of $8$ .

Cancel the common factor.

$- 16 \leq \frac{3 x - 1}{8} \cdot 8 \leq 0 \cdot 8$

Rewrite the expression.

$- 16 \leq 3 x - 1 \leq 0 \cdot 8$

Multiply $0$ by $8$ .

$- 16 \leq 3 x - 1 \leq 0$

Move all terms not containing $x$ from the center section of the inequality.

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 16 + 1 \leq 3 x \leq 0 + 1$

Add $- 16$ and $1$ .

$- 15 \leq 3 x \leq 0 + 1$

Add $0$ and $1$ .

$- 15 \leq 3 x \leq 1$

Divide each term in the inequality by $3$ .

$\frac{- 15}{3} \leq \frac{3 x}{3} \leq \frac{1}{3}$

Divide $- 15$ by $3$ .

$- 5 \leq \frac{3 x}{3} \leq \frac{1}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 5 \leq \frac{3 x}{3} \leq \frac{1}{3}$

Divide $x$ by $1$ .

$- 5 \leq x \leq \frac{1}{3}$

The result can be shown in multiple forms.

Inequality Form:

$- 5 \leq x \leq \frac{1}{3}$

Interval Notation:

$[- 5, \frac{1}{3}]$