Solve the System of Inequalities 9-x<=3+2x and 3x-7<=-22

$9 - x \leq 3 + 2 x$ and $3 x - 7 \leq - 22$

Simplify the first inequality.

Move all terms containing $x$ to the left side of the inequality.

Subtract $2 x$ from both sides of the inequality.

$9 - x - 2 x \leq 3$

Subtract $2 x$ from $- x$ .

$9 - 3 x \leq 3$

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

Subtract $9$ from both sides of the inequality.

$- 3 x \leq 3 - 9$

Subtract $9$ from $3$ .

$- 3 x \leq - 6$

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

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

$\frac{- 3 x}{- 3} \geq \frac{- 6}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 x}{- 3} \geq \frac{- 6}{- 3}$

Divide $x$ by $1$ .

$x \geq \frac{- 6}{- 3}$

Simplify the right side.

Divide $- 6$ by $- 3$ .

$x \geq 2$

Simplify the second inequality.

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

Add $7$ to both sides of the inequality.

$3 x \leq - 22 + 7$

Add $- 22$ and $7$ .

$3 x \leq - 15$

Divide each term in $3 x \leq - 15$ by $3$ and simplify.

Divide each term in $3 x \leq - 15$ by $3$ .

$\frac{3 x}{3} \leq \frac{- 15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} \leq \frac{- 15}{3}$

Divide $x$ by $1$ .

$x \leq \frac{- 15}{3}$

Simplify the right side.

Divide $- 15$ by $3$ .

$x \leq - 5$

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

No solution

Solve the System of Inequalities 9-x<=3+2x and 3x-7<=-22

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