Solve the System of Inequalities -9x+5<=17 OR 13x+25<=-1

$- 9 x + 5 \leq 17$ OR $13 x + 25 \leq - 1$

Step 1

Solve $- 9 x + 5 \leq 17$ for $x$ .

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

Subtract $5$ from both sides of the inequality.

$- 9 x \leq 17 - 5$

Subtract $5$ from $17$ .

$- 9 x \leq 12$

Divide each term in $- 9 x \leq 12$ by $- 9$ and simplify.

Divide each term in $- 9 x \leq 12$ by $- 9$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 9 x}{- 9} \geq \frac{12}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} \geq \frac{12}{- 9}$

Divide $x$ by $1$ .

$x \geq \frac{12}{- 9}$

Simplify the right side.

Cancel the common factor of $12$ and $- 9$ .

Factor $3$ out of $12$ .

$x \geq \frac{3 (4)}{- 9}$

Cancel the common factors.

Factor $3$ out of $- 9$ .

$x \geq \frac{3 \cdot 4}{3 \cdot - 3}$

Cancel the common factor.

$x \geq \frac{3 \cdot 4}{3 \cdot - 3}$

Rewrite the expression.

$x \geq \frac{4}{- 3}$

Move the negative in front of the fraction.

$x \geq - \frac{4}{3}$

Step 2

Solve $13 x + 25 \leq - 1$ for $x$ .

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

Subtract $25$ from both sides of the inequality.

$13 x \leq - 1 - 25$

Subtract $25$ from $- 1$ .

$13 x \leq - 26$

Divide each term in $13 x \leq - 26$ by $13$ and simplify.

Divide each term in $13 x \leq - 26$ by $13$ .

$\frac{13 x}{13} \leq \frac{- 26}{13}$

Simplify the left side.

Cancel the common factor of $13$ .

Cancel the common factor.

$\frac{13 x}{13} \leq \frac{- 26}{13}$

Divide $x$ by $1$ .

$x \leq \frac{- 26}{13}$

Simplify the right side.

Divide $- 26$ by $13$ .

$x \leq - 2$

Step 3

Find the intersection of $x \geq - \frac{4}{3}$ and $x \leq - 2$ .

No solution

Solve the System of Inequalities -9x+5<=17 OR 13x+25<=-1

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