Solve the Inequality for q 9q+2>-3q+1

$9 q + 2 > - 3 q + 1$

Move all terms containing $q$ to the left side of the inequality.

Add $3 q$ to both sides of the inequality.

$9 q + 2 + 3 q > 1$

Add $9 q$ and $3 q$ .

$12 q + 2 > 1$

Move all terms not containing $q$ to the right side of the inequality.

Subtract $2$ from both sides of the inequality.

$12 q > 1 - 2$

Subtract $2$ from $1$ .

$12 q > - 1$

Divide each term in $12 q > - 1$ by $12$ and simplify.

Divide each term in $12 q > - 1$ by $12$ .

$\frac{12 q}{12} > \frac{- 1}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 q}{12} > \frac{- 1}{12}$

Divide $q$ by $1$ .

$q > \frac{- 1}{12}$

Simplify the right side.

Move the negative in front of the fraction.

$q > - \frac{1}{12}$

The result can be shown in multiple forms.

Inequality Form:

$q > - \frac{1}{12}$

Interval Notation:

$(- \frac{1}{12}, \infty)$