Solve the Inequality for x -3<=2/3x-5<-1

$- 3 \leq \frac{2}{3} x - 5 < - 1$

Combine $\frac{2}{3}$ and $x$ .

$- 3 \leq \frac{2 x}{3} - 5 < - 1$

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 + 5 \leq \frac{2 x}{3} < - 1 + 5$

Add $- 3$ and $5$ .

$2 \leq \frac{2 x}{3} < - 1 + 5$

Multiply each term in the inequality by $3$ .

$2 \cdot 3 \leq \frac{2 x}{3} \cdot 3 < - 1 \cdot 3 + 5 \cdot 3$

Multiply $2$ by $3$ .

$6 \leq \frac{2 x}{3} \cdot 3 < - 1 \cdot 3 + 5 \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$6 \leq \frac{2 x}{3} \cdot 3 < - 1 \cdot 3 + 5 \cdot 3$

Rewrite the expression.

$6 \leq 2 x < - 1 \cdot 3 + 5 \cdot 3$

Simplify each term.

Multiply $- 1$ by $3$ .

$6 \leq 2 x < - 3 + 5 \cdot 3$

Multiply $5$ by $3$ .

$6 \leq 2 x < - 3 + 15$

Add $- 3$ and $15$ .

$6 \leq 2 x < 12$

Divide each term in the inequality by $2$ .

$\frac{6}{2} \leq \frac{2 x}{2} < \frac{12}{2}$

Divide $6$ by $2$ .

$3 \leq \frac{2 x}{2} < \frac{12}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 \leq \frac{2 x}{2} < \frac{12}{2}$

Divide $x$ by $1$ .

$3 \leq x < \frac{12}{2}$

Divide $12$ by $2$ .

$3 \leq x < 6$

The result can be shown in multiple forms.

Inequality Form:

$3 \leq x < 6$

Interval Notation:

$[3, 6)$