Solve for x -2<2x-2<=6

$- 2 < 2 x - 2 \leq 6$

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.

$- 2 + 2 < 2 x \leq 6 + 2$

Add $- 2$ and $2$ .

$0 < 2 x \leq 6 + 2$

Add $6$ and $2$ .

$0 < 2 x \leq 8$

Step 2

Divide each term in the inequality by $2$ .

$\frac{0}{2} < \frac{2 x}{2} \leq \frac{8}{2}$

Step 3

Divide $0$ by $2$ .

$0 < \frac{2 x}{2} \leq \frac{8}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$0 < \frac{2 x}{2} \leq \frac{8}{2}$

Divide $x$ by $1$ .

$0 < x \leq \frac{8}{2}$

Step 5

Divide $8$ by $2$ .

$0 < x \leq 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$0 < x \leq 4$

Interval Notation:

$(0, 4]$

Step 7