Solve the System of Inequalities 4x+5<-4 OR 9x-2>-17

$4 x + 5 < - 4$ OR $9 x - 2 > - 17$

Step 1

Solve $4 x + 5 < - 4$ for $x$ .

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

Subtract $5$ from both sides of the inequality.

$4 x < - 4 - 5$

Subtract $5$ from $- 4$ .

$4 x < - 9$

Divide each term in $4 x < - 9$ by $4$ and simplify.

Divide each term in $4 x < - 9$ by $4$ .

$\frac{4 x}{4} < \frac{- 9}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} < \frac{- 9}{4}$

Divide $x$ by $1$ .

$x < \frac{- 9}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x < - \frac{9}{4}$

Step 2

Solve $9 x - 2 > - 17$ for $x$ .

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

Add $2$ to both sides of the inequality.

$9 x > - 17 + 2$

Add $- 17$ and $2$ .

$9 x > - 15$

Divide each term in $9 x > - 15$ by $9$ and simplify.

Divide each term in $9 x > - 15$ by $9$ .

$\frac{9 x}{9} > \frac{- 15}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} > \frac{- 15}{9}$

Divide $x$ by $1$ .

$x > \frac{- 15}{9}$

Simplify the right side.

Cancel the common factor of $- 15$ and $9$ .

Factor $3$ out of $- 15$ .

$x > \frac{3 (- 5)}{9}$

Cancel the common factors.

Factor $3$ out of $9$ .

$x > \frac{3 \cdot - 5}{3 \cdot 3}$

Cancel the common factor.

$x > \frac{3 \cdot - 5}{3 \cdot 3}$

Rewrite the expression.

$x > \frac{- 5}{3}$

Move the negative in front of the fraction.

$x > - \frac{5}{3}$

Step 3

Find the intersection of $x < - \frac{9}{4}$ and $x > - \frac{5}{3}$ .

No solution

Solve the System of Inequalities 4x+5<-4 OR 9x-2>-17

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