Solve for x 1<2x+3<9

$1 < 2 x + 3 < 9$

Step 1

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

Subtract $3$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$1 - 3 < 2 x < 9 - 3$

Subtract $3$ from $1$ .

$- 2 < 2 x < 9 - 3$

Subtract $3$ from $9$ .

$- 2 < 2 x < 6$

Step 2

Divide each term in the inequality by $2$ .

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

Step 3

Divide $- 2$ by $2$ .

$- 1 < \frac{2 x}{2} < \frac{6}{2}$

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

$- 1 < \frac{2 x}{2} < \frac{6}{2}$

Divide $x$ by $1$ .

$- 1 < x < \frac{6}{2}$

Step 5

Divide $6$ by $2$ .

$- 1 < x < 3$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x < 3$

Interval Notation:

$(- 1, 3)$

Step 7