Solve the System of Inequalities 15>2x-9>-23

$15 > 2 x - 9 > - 23$

Step 1

Solve $15 > 2 x - 9$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$2 x - 9 < 15$

Move all terms not containing $x$ to the right side of the inequality.

Add $9$ to both sides of the inequality.

$2 x < 15 + 9$

Add $15$ and $9$ .

$2 x < 24$

Divide each term in $2 x < 24$ by $2$ and simplify.

Divide each term in $2 x < 24$ by $2$ .

$\frac{2 x}{2} < \frac{24}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{24}{2}$

Divide $x$ by $1$ .

$x < \frac{24}{2}$

Simplify the right side.

Divide $24$ by $2$ .

$x < 12$

Step 2

Solve $2 x - 9 > - 23$ for $x$ .

Move all terms not containing $x$ to the right side of the inequality.

Add $9$ to both sides of the inequality.

$2 x > - 23 + 9$

Add $- 23$ and $9$ .

$2 x > - 14$

Divide each term in $2 x > - 14$ by $2$ and simplify.

Divide each term in $2 x > - 14$ by $2$ .

$\frac{2 x}{2} > \frac{- 14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 14}{2}$

Divide $x$ by $1$ .

$x > \frac{- 14}{2}$

Simplify the right side.

Divide $- 14$ by $2$ .

$x > - 7$

Step 3

Find the intersection of $x < 12$ and $x > - 7$ .

$- 7 < x < 12$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 7 < x < 12$

Interval Notation:

$(- 7, 12)$

Step 5

Solve the System of Inequalities 15>2x-9>-23

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