Solve the System of Inequalities -9x+2>18 ; AND , 13x+15<=-4

$- 9 x + 2 > 18$ ; AND , $13 x + 15 \leq - 4$

Step 1

Solve $- 9 x + 2 > 18$ for $x$ .

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

Subtract $2$ from both sides of the inequality.

$- 9 x > 18 - 2$

Subtract $2$ from $18$ .

$- 9 x > 16$

Divide each term in $- 9 x > 16$ by $- 9$ and simplify.

Divide each term in $- 9 x > 16$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} < \frac{16}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} < \frac{16}{- 9}$

Divide $x$ by $1$ .

$x < \frac{16}{- 9}$

Simplify the right side.

Move the negative in front of the fraction.

$x < - \frac{16}{9}$

Step 2

Solve $13 x + 15 \leq - 4$ for $x$ .

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

Subtract $15$ from both sides of the inequality.

$13 x \leq - 4 - 15$

Subtract $15$ from $- 4$ .

$13 x \leq - 19$

Divide each term in $13 x \leq - 19$ by $13$ and simplify.

Divide each term in $13 x \leq - 19$ by $13$ .

$\frac{13 x}{13} \leq \frac{- 19}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} \leq \frac{- 19}{13}$

Divide $x$ by $1$ .

$x \leq \frac{- 19}{13}$

Simplify the right side.

Move the negative in front of the fraction.

$x \leq - \frac{19}{13}$

Step 3

Find the intersection of $x < - \frac{16}{9}$ and $x \leq - \frac{19}{13}$ .

$x < - \frac{16}{9}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < - \frac{16}{9}$

Interval Notation:

$(- \infty, - \frac{16}{9})$

Step 5

Solve the System of Inequalities -9x+2>18 ; AND , 13x+15<=-4

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