Solve for x -7<=2x-5<=3

$- 7 \leq 2 x - 5 \leq 3$

Step 1

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 7 + 5 \leq 2 x \leq 3 + 5$

Add $- 7$ and $5$ .

$- 2 \leq 2 x \leq 3 + 5$

Add $3$ and $5$ .

$- 2 \leq 2 x \leq 8$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 2$ by $2$ .

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Step 5

Divide $8$ by $2$ .

$- 1 \leq x \leq 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 \leq x \leq 4$

Interval Notation:

$[- 1, 4]$

Step 7