Solve for x 2<2x-2<=8

$2 < 2 x - 2 \leq 8$

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.

$2 + 2 < 2 x \leq 8 + 2$

Add $2$ and $2$ .

$4 < 2 x \leq 8 + 2$

Add $8$ and $2$ .

$4 < 2 x \leq 10$

Step 2

Divide each term in the inequality by $2$ .

$\frac{4}{2} < \frac{2 x}{2} \leq \frac{10}{2}$

Step 3

Divide $4$ by $2$ .

$2 < \frac{2 x}{2} \leq \frac{10}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$2 < \frac{2 x}{2} \leq \frac{10}{2}$

Divide $x$ by $1$ .

$2 < x \leq \frac{10}{2}$

Step 5

Divide $10$ by $2$ .

$2 < x \leq 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$2 < x \leq 5$

Interval Notation:

$(2, 5]$

Step 7