Precalculus Examples

$- 67 < - 2 w + 5 + 11 w < 50$

Step 1

Add $- 2 w$ and $11 w$ .

$- 67 < 9 w + 5 < 50$

Step 2

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

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Step 2.1

Subtract $5$ from each section of the inequality because it does not contain the variable we are trying to solve for.

$- 67 - 5 < 9 w < 50 - 5$

Step 2.2

Subtract $5$ from $- 67$ .

$- 72 < 9 w < 50 - 5$

Step 2.3

Subtract $5$ from $50$ .

$- 72 < 9 w < 45$

Step 3

Divide each term in the inequality by $9$ .

$\frac{- 72}{9} < \frac{9 w}{9} < \frac{45}{9}$

Step 4

Divide $- 72$ by $9$ .

$- 8 < \frac{9 w}{9} < \frac{45}{9}$

Step 5

Cancel the common factor of $9$ .

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Step 5.1

Cancel the common factor.

$- 8 < \frac{9 w}{9} < \frac{45}{9}$

Step 5.2

Divide $w$ by $1$ .

$- 8 < w < \frac{45}{9}$

Step 6

Divide $45$ by $9$ .

$- 8 < w < 5$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$- 8 < w < 5$

Interval Notation:

$(- 8, 5)$

Step 8