Solve for y -3<=2y+1<=9

$- 3 \leq 2 y + 1 \leq 9$

Step 1

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

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

$- 3 - 1 \leq 2 y \leq 9 - 1$

Subtract $1$ from $- 3$ .

$- 4 \leq 2 y \leq 9 - 1$

Subtract $1$ from $9$ .

$- 4 \leq 2 y \leq 8$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 4}{2} \leq \frac{2 y}{2} \leq \frac{8}{2}$

Step 3

Divide $- 4$ by $2$ .

$- 2 \leq \frac{2 y}{2} \leq \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 2 \leq \frac{2 y}{2} \leq \frac{8}{2}$

Divide $y$ by $1$ .

$- 2 \leq y \leq \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

$- 2 \leq y \leq 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 2 \leq y \leq 4$

Interval Notation:

$[- 2, 4]$

Step 7