Solve the Inequality for w -w+9>6w+8

$- w + 9 > 6 w + 8$

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

Subtract $6 w$ from both sides of the inequality.

$- w + 9 - 6 w > 8$

Subtract $6 w$ from $- w$ .

$- 7 w + 9 > 8$

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

Subtract $9$ from both sides of the inequality.

$- 7 w > 8 - 9$

Subtract $9$ from $8$ .

$- 7 w > - 1$

Divide each term in $- 7 w > - 1$ by $- 7$ and simplify.

Divide each term in $- 7 w > - 1$ by $- 7$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 7 w}{- 7} < \frac{- 1}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 w}{- 7} < \frac{- 1}{- 7}$

Divide $w$ by $1$ .

$w < \frac{- 1}{- 7}$

Simplify the right side.

Dividing two negative values results in a positive value.

$w < \frac{1}{7}$

The result can be shown in multiple forms.

Inequality Form:

$w < \frac{1}{7}$

Interval Notation:

$(- \infty, \frac{1}{7})$

Solve the Inequality for w -w+9>6w+8

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