Solve for x -4<2x-2<6

$- 4 < 2 x - 2 < 6$

Step 1

Move all terms not containing $x$ 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.

$- 4 + 2 < 2 x < 6 + 2$

Add $- 4$ and $2$ .

$- 2 < 2 x < 6 + 2$

Add $6$ and $2$ .

$- 2 < 2 x < 8$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 2}{2} < \frac{2 x}{2} < \frac{8}{2}$

Step 3

Divide $- 2$ by $2$ .

$- 1 < \frac{2 x}{2} < \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 < \frac{2 x}{2} < \frac{8}{2}$

Divide $x$ by $1$ .

$- 1 < x < \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

$- 1 < x < 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x < 4$

Interval Notation:

$(- 1, 4)$

Step 7