Algebra Examples

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

Step 1

Multiply each term in the inequality by $3$ .

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

Step 2

Multiply $3$ by $3$ .

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Multiply $3$ by $1$ .

$9 \geq 9 - w > 3$

Step 5

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

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Step 5.1

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

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

Step 5.2

Subtract $9$ from $9$ .

$0 \geq - w > 3 - 9$

Step 5.3

Subtract $9$ from $3$ .

$0 \geq - w > - 6$

Step 6

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

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

Step 7

Divide $0$ by $- 1$ .

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

Step 8

Dividing two negative values results in a positive value.

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

Step 9

Divide $w$ by $1$ .

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

Step 10

Divide $- 6$ by $- 1$ .

$0 \leq w < 6$

Step 11

Convert the inequality to interval notation.

$[0, 6)$

Step 12