Finite Math Examples

$14 > \frac{5}{9} w + 4$

Step 1

Rewrite so $w$ is on the left side of the inequality.

$\frac{5}{9} w + 4 < 14$

Step 2

Combine $\frac{5}{9}$ and $w$ .

$\frac{5 w}{9} + 4 < 14$

Step 3

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

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Step 3.1

Subtract $4$ from both sides of the inequality.

$\frac{5 w}{9} < 14 - 4$

Step 3.2

Subtract $4$ from $14$ .

$\frac{5 w}{9} < 10$

Step 4

Multiply both sides by $9$ .

$\frac{5 w}{9} \cdot 9 < 10 \cdot 9$

Step 5

Simplify.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Cancel the common factor of $9$ .

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Step 5.1.1.1

Cancel the common factor.

$\frac{5 w}{9} \cdot 9 < 10 \cdot 9$

Step 5.1.1.2

Rewrite the expression.

$5 w < 10 \cdot 9$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $10$ by $9$ .

$5 w < 90$

Step 6

Divide each term in $5 w < 90$ by $5$ and simplify.

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Step 6.1

Divide each term in $5 w < 90$ by $5$ .

$\frac{5 w}{5} < \frac{90}{5}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $5$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{5 w}{5} < \frac{90}{5}$

Step 6.2.1.2

Divide $w$ by $1$ .

$w < \frac{90}{5}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $90$ by $5$ .

$w < 18$

Step 7

The result can be shown in multiple forms.

Inequality Form:

$w < 18$

Interval Notation:

$(- \infty, 18)$