Solve the Inequality for x 9<2x+3<5

$9 < 2 x + 3 < 5$

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.

$9 - 3 < 2 x < 5 - 3$

Subtract $3$ from $9$ .

$6 < 2 x < 5 - 3$

Subtract $3$ from $5$ .

$6 < 2 x < 2$

Divide each term in the inequality by $2$ .

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

Divide $6$ by $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Divide $2$ by $2$ .

$3 < x < 1$

Since the inequality can never be true, there is no solution.

False