Solve for y 0<2y+3<=4

$0 < 2 y + 3 \leq 4$

Step 1

Move all terms not containing $y$ 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.

$0 - 3 < 2 y \leq 4 - 3$

Subtract $3$ from $0$ .

$- 3 < 2 y \leq 4 - 3$

Subtract $3$ from $4$ .

$- 3 < 2 y \leq 1$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 3}{2} < \frac{2 y}{2} \leq \frac{1}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{2} < \frac{2 y}{2} \leq \frac{1}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{3}{2} < \frac{2 y}{2} \leq \frac{1}{2}$

Divide $y$ by $1$ .

$- \frac{3}{2} < y \leq \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{2} < y \leq \frac{1}{2}$

Interval Notation:

$(- \frac{3}{2}, \frac{1}{2}]$

Step 6