Solve for x -3<=(2x+5)/3<6

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

Step 1

Multiply each term in the inequality by $3$ .

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

Step 2

Multiply $- 3$ by $3$ .

$- 9 \leq \frac{2 x + 5}{3} \cdot 3 < 6 \cdot 3$

Step 3

Cancel the common factor of $3$ .

Cancel the common factor.

$- 9 \leq \frac{2 x + 5}{3} \cdot 3 < 6 \cdot 3$

Rewrite the expression.

$- 9 \leq 2 x + 5 < 6 \cdot 3$

Step 4

Multiply $6$ by $3$ .

$- 9 \leq 2 x + 5 < 18$

Step 5

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

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

$- 9 - 5 \leq 2 x < 18 - 5$

Subtract $5$ from $- 9$ .

$- 14 \leq 2 x < 18 - 5$

Subtract $5$ from $18$ .

$- 14 \leq 2 x < 13$

Step 6

Divide each term in the inequality by $2$ .

$\frac{- 14}{2} \leq \frac{2 x}{2} < \frac{13}{2}$

Step 7

Divide $- 14$ by $2$ .

$- 7 \leq \frac{2 x}{2} < \frac{13}{2}$

Step 8

Cancel the common factor of $2$ .

Cancel the common factor.

$- 7 \leq \frac{2 x}{2} < \frac{13}{2}$

Divide $x$ by $1$ .

$- 7 \leq x < \frac{13}{2}$

Step 9

The result can be shown in multiple forms.

Inequality Form:

$- 7 \leq x < \frac{13}{2}$

Interval Notation:

$[- 7, \frac{13}{2})$

Step 10