Solve for x -11<=-5x-1<14

$- 11 \leq - 5 x - 1 < 14$

Step 1

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

Add $1$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 11 + 1 \leq - 5 x < 14 + 1$

Add $- 11$ and $1$ .

$- 10 \leq - 5 x < 14 + 1$

Add $14$ and $1$ .

$- 10 \leq - 5 x < 15$

Step 2

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

$\frac{- 10}{- 5} \geq \frac{- 5 x}{- 5} > \frac{15}{- 5}$

Step 3

Divide $- 10$ by $- 5$ .

$2 \geq \frac{- 5 x}{- 5} > \frac{15}{- 5}$

Step 4

Cancel the common factor of $- 5$ .

Cancel the common factor.

$2 \geq \frac{- 5 x}{- 5} > \frac{15}{- 5}$

Divide $x$ by $1$ .

$2 \geq x > \frac{15}{- 5}$

Step 5

Divide $15$ by $- 5$ .

$2 \geq x > - 3$

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.

$- 3 < x \leq 2$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x \leq 2$

Interval Notation:

$(- 3, 2]$

Step 8