Solve the Inequality for x -5<=-5x+5<=50

$- 5 \leq - 5 x + 5 \leq 50$

Step 1

Move all terms not containing $x$ from the center section of the inequality.

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 5 - 5 \leq - 5 x \leq 50 - 5$

Subtract $5$ from $- 5$ .

$- 10 \leq - 5 x \leq 50 - 5$

Subtract $5$ from $50$ .

$- 10 \leq - 5 x \leq 45$

Step 2

Divide each term in the inequality by $- 5$ .

$\frac{- 10}{- 5} \geq \frac{- 5 x}{- 5} \geq \frac{45}{- 5}$

Step 3

Divide $- 10$ by $- 5$ .

$2 \geq \frac{- 5 x}{- 5} \geq \frac{45}{- 5}$

Step 4

Cancel the common factor of $- 5$ .

Cancel the common factor.

$2 \geq \frac{- 5 x}{- 5} \geq \frac{45}{- 5}$

Divide $x$ by $1$ .

$2 \geq x \geq \frac{45}{- 5}$

Step 5

Divide $45$ by $- 5$ .

$2 \geq x \geq - 9$

Step 6

Rewrite the interval so that the left value is less than the right value. This is the correct way to write an interval solution.

$- 9 \leq x \leq 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 9 \leq x \leq 2$

Interval Notation:

$[- 9, 2]$

Step 8