Solve the System of Inequalities -15>-3x-9 and -3x-9<-39

$- 15 > - 3 x - 9$ and $- 3 x - 9 < - 39$

Step 1

Simplify the first inequality.

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

$- 3 x - 9 < - 15$ and $- 3 x - 9 < - 39$

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

Add $9$ to both sides of the inequality.

$- 3 x < - 15 + 9$ and $- 3 x - 9 < - 39$

Add $- 15$ and $9$ .

$- 3 x < - 6$ and $- 3 x - 9 < - 39$

Divide each term in $- 3 x < - 6$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 6$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 3 x}{- 3} > \frac{- 6}{- 3}$ and $- 3 x - 9 < - 39$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} > \frac{- 6}{- 3}$ and $- 3 x - 9 < - 39$

Divide $x$ by $1$ .

$x > \frac{- 6}{- 3}$ and $- 3 x - 9 < - 39$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x > 2$ and $- 3 x - 9 < - 39$

Step 2

Simplify the second inequality.

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

Add $9$ to both sides of the inequality.

$x > 2$ and $- 3 x < - 39 + 9$

Add $- 39$ and $9$ .

$x > 2$ and $- 3 x < - 30$

Divide each term in $- 3 x < - 30$ by $- 3$ and simplify.

Divide each term in $- 3 x < - 30$ by $- 3$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$x > 2$ and $\frac{- 3 x}{- 3} > \frac{- 30}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$x > 2$ and $\frac{- 3 x}{- 3} > \frac{- 30}{- 3}$

Divide $x$ by $1$ .

$x > 2$ and $x > \frac{- 30}{- 3}$

Simplify the right side.

Divide $- 30$ by $- 3$ .

$x > 2$ and $x > 10$

Step 3

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

$x > 10$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 10$

Interval Notation:

$(10, \infty)$

Step 5

Solve the System of Inequalities -15>-3x-9 and -3x-9<-39

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