Solve the Inequality for x -1<=(2x+3)/3<4

$- 1 \leq \frac{2 x + 3}{3} < 4$

Multiply each term in the inequality by $3$ .

$- 1 \cdot 3 \leq \frac{2 x + 3}{3} \cdot 3 < 4 \cdot 3$

Multiply $- 1$ by $3$ .

$- 3 \leq \frac{2 x + 3}{3} \cdot 3 < 4 \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 3 \leq \frac{2 x + 3}{3} \cdot 3 < 4 \cdot 3$

Rewrite the expression.

$- 3 \leq 2 x + 3 < 4 \cdot 3$

Multiply $4$ by $3$ .

$- 3 \leq 2 x + 3 < 12$

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 - 3 \leq 2 x < 12 - 3$

Subtract $3$ from $- 3$ .

$- 6 \leq 2 x < 12 - 3$

Subtract $3$ from $12$ .

$- 6 \leq 2 x < 9$

Divide each term in the inequality by $2$ .

$\frac{- 6}{2} \leq \frac{2 x}{2} < \frac{9}{2}$

Divide $- 6$ by $2$ .

$- 3 \leq \frac{2 x}{2} < \frac{9}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$- 3 \leq \frac{2 x}{2} < \frac{9}{2}$

Divide $x$ by $1$ .

$- 3 \leq x < \frac{9}{2}$

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x < \frac{9}{2}$

Interval Notation:

$[- 3, \frac{9}{2})$