Solve the Inequality for w w+9<-6w+3

$w + 9 < - 6 w + 3$

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

Add $6 w$ to both sides of the inequality.

$w + 9 + 6 w < 3$

Add $w$ and $6 w$ .

$7 w + 9 < 3$

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

Subtract $9$ from both sides of the inequality.

$7 w < 3 - 9$

Subtract $9$ from $3$ .

$7 w < - 6$

Divide each term in $7 w < - 6$ by $7$ and simplify.

Divide each term in $7 w < - 6$ by $7$ .

$\frac{7 w}{7} < \frac{- 6}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 w}{7} < \frac{- 6}{7}$

Divide $w$ by $1$ .

$w < \frac{- 6}{7}$

Simplify the right side.

Move the negative in front of the fraction.

$w < - \frac{6}{7}$

The result can be shown in multiple forms.

Inequality Form:

$w < - \frac{6}{7}$

Interval Notation:

$(- \infty, - \frac{6}{7})$