Solve for x -7<-2x+1<13

$- 7 < - 2 x + 1 < 13$

Step 1

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

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

$- 7 - 1 < - 2 x < 13 - 1$

Subtract $1$ from $- 7$ .

$- 8 < - 2 x < 13 - 1$

Subtract $1$ from $13$ .

$- 8 < - 2 x < 12$

Step 2

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

$\frac{- 8}{- 2} > \frac{- 2 x}{- 2} > \frac{12}{- 2}$

Step 3

Divide $- 8$ by $- 2$ .

$4 > \frac{- 2 x}{- 2} > \frac{12}{- 2}$

Step 4

Cancel the common factor of $- 2$ .

Cancel the common factor.

$4 > \frac{- 2 x}{- 2} > \frac{12}{- 2}$

Divide $x$ by $1$ .

$4 > x > \frac{12}{- 2}$

Step 5

Divide $12$ by $- 2$ .

$4 > x > - 6$

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.

$- 6 < x < 4$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 6 < x < 4$

Interval Notation:

$(- 6, 4)$

Step 8