Solve for x -5<=2x-2<=8

$- 5 \leq 2 x - 2 \leq 8$

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.

$- 5 + 2 \leq 2 x \leq 8 + 2$

Add $- 5$ and $2$ .

$- 3 \leq 2 x \leq 8 + 2$

Add $8$ and $2$ .

$- 3 \leq 2 x \leq 10$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 3}{2} \leq \frac{2 x}{2} \leq \frac{10}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{3}{2} \leq \frac{2 x}{2} \leq \frac{10}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{3}{2} \leq \frac{2 x}{2} \leq \frac{10}{2}$

Divide $x$ by $1$ .

$- \frac{3}{2} \leq x \leq \frac{10}{2}$

Step 5

Divide $10$ by $2$ .

$- \frac{3}{2} \leq x \leq 5$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{3}{2} \leq x \leq 5$

Interval Notation:

$[- \frac{3}{2}, 5]$

Step 7