Solve for x 1<2x+7<13

$1 < 2 x + 7 < 13$

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.

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

Subtract $7$ from $1$ .

$- 6 < 2 x < 13 - 7$

Subtract $7$ from $13$ .

$- 6 < 2 x < 6$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 6$ by $2$ .

$- 3 < \frac{2 x}{2} < \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 3 < \frac{2 x}{2} < \frac{6}{2}$

Divide $x$ by $1$ .

$- 3 < x < \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$- 3 < x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x < 3$

Interval Notation:

$(- 3, 3)$

Step 7