Solve for x -38<=9x-11<34

$- 38 \leq 9 x - 11 < 34$

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

Add $11$ to each section of the inequality because it does not contain the variable we are trying to solve for.

$- 38 + 11 \leq 9 x < 34 + 11$

Add $- 38$ and $11$ .

$- 27 \leq 9 x < 34 + 11$

Add $34$ and $11$ .

$- 27 \leq 9 x < 45$

Divide each term in the inequality by $9$ .

$\frac{- 27}{9} \leq \frac{9 x}{9} < \frac{45}{9}$

Divide $- 27$ by $9$ .

$- 3 \leq \frac{9 x}{9} < \frac{45}{9}$

Cancel the common factor of $9$ .

Cancel the common factor.

$- 3 \leq \frac{9 x}{9} < \frac{45}{9}$

Divide $x$ by $1$ .

$- 3 \leq x < \frac{45}{9}$

Divide $45$ by $9$ .

$- 3 \leq x < 5$

The result can be shown in multiple forms.

Inequality Form:

$- 3 \leq x < 5$

Interval Notation:

$[- 3, 5)$