Solve the System of Inequalities -15x+60<=105 ; AND , 14x+11<=-31

$- 15 x + 60 \leq 105$ ; AND , $14 x + 11 \leq - 31$

Step 1

Solve $- 15 x + 60 \leq 105$ for $x$ .

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

Subtract $60$ from both sides of the inequality.

$- 15 x \leq 105 - 60$

Subtract $60$ from $105$ .

$- 15 x \leq 45$

Divide each term in $- 15 x \leq 45$ by $- 15$ and simplify.

Divide each term in $- 15 x \leq 45$ by $- 15$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 15 x}{- 15} \geq \frac{45}{- 15}$

Simplify the left side.

Cancel the common factor of $- 15$ .

Cancel the common factor.

$\frac{- 15 x}{- 15} \geq \frac{45}{- 15}$

Divide $x$ by $1$ .

$x \geq \frac{45}{- 15}$

Simplify the right side.

Divide $45$ by $- 15$ .

$x \geq - 3$

Step 2

Solve $14 x + 11 \leq - 31$ for $x$ .

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

Subtract $11$ from both sides of the inequality.

$14 x \leq - 31 - 11$

Subtract $11$ from $- 31$ .

$14 x \leq - 42$

Divide each term in $14 x \leq - 42$ by $14$ and simplify.

Divide each term in $14 x \leq - 42$ by $14$ .

$\frac{14 x}{14} \leq \frac{- 42}{14}$

Simplify the left side.

Cancel the common factor of $14$ .

Cancel the common factor.

$\frac{14 x}{14} \leq \frac{- 42}{14}$

Divide $x$ by $1$ .

$x \leq \frac{- 42}{14}$

Simplify the right side.

Divide $- 42$ by $14$ .

$x \leq - 3$

Step 3

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

$x = - 3$

Step 4

Solve the System of Inequalities -15x+60<=105 ; AND , 14x+11<=-31

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