Solve the Inequality for w 3>=(9-w)/3>1

$3 \geq \frac{9 - w}{3} > 1$

Multiply each term in the inequality by $3$ .

$3 \cdot 3 \geq \frac{9 - w}{3} \cdot 3 > 1 \cdot 3$

Multiply $3$ by $3$ .

$9 \geq \frac{9 - w}{3} \cdot 3 > 1 \cdot 3$

Cancel the common factor of $3$ .

Cancel the common factor.

$9 \geq \frac{9 - w}{3} \cdot 3 > 1 \cdot 3$

Rewrite the expression.

$9 \geq 9 - w > 1 \cdot 3$

Multiply $3$ by $1$ .

$9 \geq 9 - w > 3$

Move all terms not containing $w$ 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.

$9 - 9 \geq - w > 3 - 9$

Subtract $9$ from $9$ .

$0 \geq - w > 3 - 9$

Subtract $9$ from $3$ .

$0 \geq - w > - 6$

Multiply each term in the inequality by $- 1$ .

$\frac{0}{- 1} \leq \frac{- w}{- 1} < \frac{- 6}{- 1}$

Divide $0$ by $- 1$ .

$0 \leq \frac{- w}{- 1} < \frac{- 6}{- 1}$

Dividing two negative values results in a positive value.

$0 \leq \frac{w}{1} < \frac{- 6}{- 1}$

Divide $w$ by $1$ .

$0 \leq w < \frac{- 6}{- 1}$

Divide $- 6$ by $- 1$ .

$0 \leq w < 6$

The result can be shown in multiple forms.

Inequality Form:

$0 \leq w < 6$

Interval Notation:

$[0, 6)$