Finite Math Examples

$- 8 + 9 > 5 (9 - x)$

Step 1

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

$5 (9 - x) < - 8 + 9$

Step 2

Add $- 8$ and $9$ .

$5 (9 - x) < 1$

Step 3

Divide each term in $5 (9 - x) < 1$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 (9 - x) < 1$ by $5$ .

$\frac{5 (9 - x)}{5} < \frac{1}{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 (9 - x)}{5} < \frac{1}{5}$

Step 3.2.1.2

Divide $9 - x$ by $1$ .

$9 - x < \frac{1}{5}$

Step 4

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

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Step 4.1

Subtract $9$ from both sides of the inequality.

$- x < \frac{1}{5} - 9$

Step 4.2

To write $- 9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- x < \frac{1}{5} - 9 \cdot \frac{5}{5}$

Step 4.3

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

$- x < \frac{1}{5} + \frac{- 9 \cdot 5}{5}$

Step 4.4

Combine the numerators over the common denominator.

$- x < \frac{1 - 9 \cdot 5}{5}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 9$ by $5$ .

$- x < \frac{1 - 45}{5}$

Step 4.5.2

Subtract $45$ from $1$ .

$- x < \frac{- 44}{5}$

Step 4.6

Move the negative in front of the fraction.

$- x < - \frac{44}{5}$

Step 5

Divide each term in $- x < - \frac{44}{5}$ by $- 1$ and simplify.

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Step 5.1

Divide each term in $- x < - \frac{44}{5}$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- \frac{44}{5}}{- 1}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- \frac{44}{5}}{- 1}$

Step 5.2.2

Divide $x$ by $1$ .

$x > \frac{- \frac{44}{5}}{- 1}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Dividing two negative values results in a positive value.

$x > \frac{\frac{44}{5}}{1}$

Step 5.3.2

Divide $\frac{44}{5}$ by $1$ .

$x > \frac{44}{5}$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$x > \frac{44}{5}$

Interval Notation:

$(\frac{44}{5}, \infty)$