Solve for y 4<2y-2<10

$4 < 2 y - 2 < 10$

Step 1

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

Add $2$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$4 + 2 < 2 y < 10 + 2$

Add $4$ and $2$ .

$6 < 2 y < 10 + 2$

Add $10$ and $2$ .

$6 < 2 y < 12$

Step 2

Divide each term in the inequality by $2$ .

$\frac{6}{2} < \frac{2 y}{2} < \frac{12}{2}$

Step 3

Divide $6$ by $2$ .

$3 < \frac{2 y}{2} < \frac{12}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$3 < \frac{2 y}{2} < \frac{12}{2}$

Divide $y$ by $1$ .

$3 < y < \frac{12}{2}$

Step 5

Divide $12$ by $2$ .

$3 < y < 6$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$3 < y < 6$

Interval Notation:

$(3, 6)$

Step 7