Solve for x 3<-2x-1<=7

$3 < - 2 x - 1 \leq 7$

Step 1

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$3 + 1 < - 2 x \leq 7 + 1$

Add $3$ and $1$ .

$4 < - 2 x \leq 7 + 1$

Add $7$ and $1$ .

$4 < - 2 x \leq 8$

Step 2

Divide each term in the inequality by $- 2$ .

$\frac{4}{- 2} > \frac{- 2 x}{- 2} \geq \frac{8}{- 2}$

Step 3

Divide $4$ by $- 2$ .

$- 2 > \frac{- 2 x}{- 2} \geq \frac{8}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$- 2 > \frac{- 2 x}{- 2} \geq \frac{8}{- 2}$

Divide $x$ by $1$ .

$- 2 > x \geq \frac{8}{- 2}$

Step 5

Divide $8$ by $- 2$ .

$- 2 > x \geq - 4$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 4 \leq x < - 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 4 \leq x < - 2$

Interval Notation:

$[- 4, - 2)$

Step 8