Convert to Set Notation 9<=2x+5<=17

$9 \leq 2 x + 5 \leq 17$

Solve $2 \leq x \leq 6$ .

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

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

$9 - 5 \leq 2 x \leq 17 - 5$

Subtract $5$ from $9$ .

$4 \leq 2 x \leq 17 - 5$

Subtract $5$ from $17$ .

$4 \leq 2 x \leq 12$

Divide each term in the inequality by $2$ .

$\frac{4}{2} \leq \frac{2 x}{2} \leq \frac{12}{2}$

Divide $4$ by $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $12$ by $2$ .

$2 \leq x \leq 6$

Use the inequality $2 \leq x \leq 6$ to build the set notation.

${x | 2 \leq x \leq 6}$