Solve for x -16<5x-1<=-11

$- 16 < 5 x - 1 \leq - 11$

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.

$- 16 + 1 < 5 x \leq - 11 + 1$

Add $- 16$ and $1$ .

$- 15 < 5 x \leq - 11 + 1$

Add $- 11$ and $1$ .

$- 15 < 5 x \leq - 10$

Step 2

Divide each term in the inequality by $5$ .

$\frac{- 15}{5} < \frac{5 x}{5} \leq \frac{- 10}{5}$

Step 3

Divide $- 15$ by $5$ .

$- 3 < \frac{5 x}{5} \leq \frac{- 10}{5}$

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

$- 3 < \frac{5 x}{5} \leq \frac{- 10}{5}$

Divide $x$ by $1$ .

$- 3 < x \leq \frac{- 10}{5}$

Step 5

Divide $- 10$ by $5$ .

$- 3 < x \leq - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x \leq - 2$

Interval Notation:

$(- 3, - 2]$

Step 7