Solve for x -28<9x-1<=-19

$- 28 < 9 x - 1 \leq - 19$

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.

$- 28 + 1 < 9 x \leq - 19 + 1$

Add $- 28$ and $1$ .

$- 27 < 9 x \leq - 19 + 1$

Add $- 19$ and $1$ .

$- 27 < 9 x \leq - 18$

Step 2

Divide each term in the inequality by $9$ .

$\frac{- 27}{9} < \frac{9 x}{9} \leq \frac{- 18}{9}$

Step 3

Divide $- 27$ by $9$ .

$- 3 < \frac{9 x}{9} \leq \frac{- 18}{9}$

Step 4

Cancel the common factor of $9$ .

Cancel the common factor.

$- 3 < \frac{9 x}{9} \leq \frac{- 18}{9}$

Divide $x$ by $1$ .

$- 3 < x \leq \frac{- 18}{9}$

Step 5

Divide $- 18$ by $9$ .

$- 3 < x \leq - 2$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$- 3 < x \leq - 2$

Interval Notation:

$(- 3, - 2]$

Step 7