Convert to Set Notation -3<2x-5<7

$- 3 < 2 x - 5 < 7$

Solve $1 < x < 6$ .

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

Add $5$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 3 + 5 < 2 x < 7 + 5$

Add $- 3$ and $5$ .

$2 < 2 x < 7 + 5$

Add $7$ and $5$ .

$2 < 2 x < 12$

Divide each term in the inequality by $2$ .

$\frac{2}{2} < \frac{2 x}{2} < \frac{12}{2}$

Divide $2$ by $2$ .

$1 < \frac{2 x}{2} < \frac{12}{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$1 < \frac{2 x}{2} < \frac{12}{2}$

Divide $x$ by $1$ .

$1 < x < \frac{12}{2}$

Divide $12$ by $2$ .

$1 < x < 6$

Use the inequality $1 < x < 6$ to build the set notation.

${x | 1 < x < 6}$