Solve for x -6<=2x+5<=7

$- 6 \leq 2 x + 5 \leq 7$

Step 1

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

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

$- 6 - 5 \leq 2 x \leq 7 - 5$

Subtract $5$ from $- 6$ .

$- 11 \leq 2 x \leq 7 - 5$

Subtract $5$ from $7$ .

$- 11 \leq 2 x \leq 2$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 11}{2} \leq \frac{2 x}{2} \leq \frac{2}{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{11}{2} \leq \frac{2 x}{2} \leq \frac{2}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- \frac{11}{2} \leq \frac{2 x}{2} \leq \frac{2}{2}$

Divide $x$ by $1$ .

$- \frac{11}{2} \leq x \leq \frac{2}{2}$

Step 5

Divide $2$ by $2$ .

$- \frac{11}{2} \leq x \leq 1$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- \frac{11}{2} \leq x \leq 1$

Interval Notation:

$[- \frac{11}{2}, 1]$

Step 7