Solve for x -12<3x+9<42

$- 12 < 3 x + 9 < 42$

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

Subtract $9$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 12 - 9 < 3 x < 42 - 9$

Subtract $9$ from $- 12$ .

$- 21 < 3 x < 42 - 9$

Subtract $9$ from $42$ .

$- 21 < 3 x < 33$

Divide each term in the inequality by $3$ .

$\frac{- 21}{3} < \frac{3 x}{3} < \frac{33}{3}$

Divide $- 21$ by $3$ .

$- 7 < \frac{3 x}{3} < \frac{33}{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$- 7 < \frac{3 x}{3} < \frac{33}{3}$

Divide $x$ by $1$ .

$- 7 < x < \frac{33}{3}$

Divide $33$ by $3$ .

$- 7 < x < 11$

The result can be shown in multiple forms.

Inequality Form:

$- 7 < x < 11$

Interval Notation:

$(- 7, 11)$