Solve the System of Inequalities 2x>-10 and 9x<18

$2 x > - 10$ and $9 x < 18$

Step 1

Divide each term in $2 x > - 10$ by $2$ and simplify.

Divide each term in $2 x > - 10$ by $2$ .

$\frac{2 x}{2} > \frac{- 10}{2}$ and $9 x < 18$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} > \frac{- 10}{2}$ and $9 x < 18$

Divide $x$ by $1$ .

$x > \frac{- 10}{2}$ and $9 x < 18$

Simplify the right side.

Divide $- 10$ by $2$ .

$x > - 5$ and $9 x < 18$

Step 2

Divide each term in $9 x < 18$ by $9$ and simplify.

Divide each term in $9 x < 18$ by $9$ .

$x > - 5$ and $\frac{9 x}{9} < \frac{18}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$x > - 5$ and $\frac{9 x}{9} < \frac{18}{9}$

Divide $x$ by $1$ .

$x > - 5$ and $x < \frac{18}{9}$

Simplify the right side.

Divide $18$ by $9$ .

$x > - 5$ and $x < 2$

Step 3

The intersection consists of the elements that are contained in both intervals.

$- 5 < x < 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$- 5 < x < 2$

Interval Notation:

$(- 5, 2)$

Step 5