Solve the System of Inequalities -3<3x<=9

$- 3 < 3 x \leq 9$

Solve $- 3 < 3 x$ for $x$ .

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

$3 x > - 3$

Divide each term in $3 x > - 3$ by $3$ and simplify.

Divide each term in $3 x > - 3$ by $3$ .

$\frac{3 x}{3} > \frac{- 3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} > \frac{- 3}{3}$

Divide $x$ by $1$ .

$x > \frac{- 3}{3}$

Simplify the right side.

Divide $- 3$ by $3$ .

$x > - 1$

Divide each term in $3 x \leq 9$ by $3$ and simplify.

Divide each term in $3 x \leq 9$ by $3$ .

$\frac{3 x}{3} \leq \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{9}{3}$

Divide $x$ by $1$ .

$x \leq \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

$x \leq 3$

Find the intersection of $x > - 1$ and $x \leq 3$ .

$- 1 < x \leq 3$

The result can be shown in multiple forms.

Inequality Form:

$- 1 < x \leq 3$

Interval Notation:

$(- 1, 3]$