Solve the System of Inequalities -8>=-5x+7>=-33

$- 8 \geq - 5 x + 7 \geq - 33$

Solve $- 8 \geq - 5 x + 7$ for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$- 5 x + 7 \leq - 8$

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

Subtract $7$ from both sides of the inequality.

$- 5 x \leq - 8 - 7$

Subtract $7$ from $- 8$ .

$- 5 x \leq - 15$

Divide each term in $- 5 x \leq - 15$ by $- 5$ and simplify.

Divide each term in $- 5 x \leq - 15$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \geq \frac{- 15}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \geq \frac{- 15}{- 5}$

Divide $x$ by $1$ .

$x \geq \frac{- 15}{- 5}$

Simplify the right side.

Divide $- 15$ by $- 5$ .

$x \geq 3$

Solve $- 5 x + 7 \geq - 33$ for $x$ .

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

Subtract $7$ from both sides of the inequality.

$- 5 x \geq - 33 - 7$

Subtract $7$ from $- 33$ .

$- 5 x \geq - 40$

Divide each term in $- 5 x \geq - 40$ by $- 5$ and simplify.

Divide each term in $- 5 x \geq - 40$ by $- 5$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 5 x}{- 5} \leq \frac{- 40}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} \leq \frac{- 40}{- 5}$

Divide $x$ by $1$ .

$x \leq \frac{- 40}{- 5}$

Simplify the right side.

Divide $- 40$ by $- 5$ .

$x \leq 8$

Find the intersection of $x \geq 3$ and $x \leq 8$ .

$3 \leq x \leq 8$

The result can be shown in multiple forms.

Inequality Form:

$3 \leq x \leq 8$

Interval Notation:

$[3, 8]$

Solve the System of Inequalities -8>=-5x+7>=-33

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