Solve for x 3<2x+1<7

$3 < 2 x + 1 < 7$

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.

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

Subtract $1$ from $3$ .

$2 < 2 x < 7 - 1$

Subtract $1$ from $7$ .

$2 < 2 x < 6$

Divide each term in the inequality by $2$ .

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

Divide $2$ by $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $6$ by $2$ .

$1 < x < 3$

The result can be shown in multiple forms.

Inequality Form:

$1 < x < 3$

Interval Notation:

$(1, 3)$