Solve for x -1<=2x+7<1

$- 1 \leq 2 x + 7 < 1$

Step 1

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

Subtract $7$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 1 - 7 \leq 2 x < 1 - 7$

Subtract $7$ from $- 1$ .

$- 8 \leq 2 x < 1 - 7$

Subtract $7$ from $1$ .

$- 8 \leq 2 x < - 6$

Step 2

Divide each term in the inequality by $2$ .

$\frac{- 8}{2} \leq \frac{2 x}{2} < \frac{- 6}{2}$

Step 3

Divide $- 8$ by $2$ .

$- 4 \leq \frac{2 x}{2} < \frac{- 6}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 4 \leq \frac{2 x}{2} < \frac{- 6}{2}$

Divide $x$ by $1$ .

$- 4 \leq x < \frac{- 6}{2}$

Step 5

Divide $- 6$ by $2$ .

$- 4 \leq x < - 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x < - 3$

Interval Notation:

$[- 4, - 3)$

Step 7