Finite Math Examples

$r (9) = \frac{6}{x - 8}$

Step 1

Rewrite the equation as $\frac{6}{x - 8} = r (9)$ .

$\frac{6}{x - 8} = r (9)$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x - 8, 1$

Step 2.2

Remove parentheses.

$x - 8, 1$

Step 2.3

The LCM of one and any expression is the expression.

$x - 8$

Step 3

Multiply each term in $\frac{6}{x - 8} = r (9)$ by $x - 8$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{6}{x - 8} = r (9)$ by $x - 8$ .

$\frac{6}{x - 8} (x - 8) = r (9) (x - 8)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $x - 8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6}{x - 8} (x - 8) = r (9) (x - 8)$

Step 3.2.1.2

Rewrite the expression.

$6 = r (9) (x - 8)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Move $9$ to the left of $r$ .

$6 = 9 r (x - 8)$

Step 3.3.2

Apply the distributive property.

$6 = 9 r x + 9 r \cdot - 8$

Step 3.3.3

Multiply $- 8$ by $9$ .

$6 = 9 r x - 72 r$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as $9 r x - 72 r = 6$ .

$9 r x - 72 r = 6$

Step 4.2

Add $72 r$ to both sides of the equation.

$9 r x = 6 + 72 r$

Step 4.3

Divide each term in $9 r x = 6 + 72 r$ by $9 r$ and simplify.

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Step 4.3.1

Divide each term in $9 r x = 6 + 72 r$ by $9 r$ .

$\frac{9 r x}{9 r} = \frac{6}{9 r} + \frac{72 r}{9 r}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $9$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{9 r x}{9 r} = \frac{6}{9 r} + \frac{72 r}{9 r}$

Step 4.3.2.1.2

Rewrite the expression.

$\frac{r x}{r} = \frac{6}{9 r} + \frac{72 r}{9 r}$

Step 4.3.2.2

Cancel the common factor of $r$ .

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Step 4.3.2.2.1

Cancel the common factor.

$\frac{r x}{r} = \frac{6}{9 r} + \frac{72 r}{9 r}$

Step 4.3.2.2.2

Divide $x$ by $1$ .

$x = \frac{6}{9 r} + \frac{72 r}{9 r}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Simplify each term.

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Step 4.3.3.1.1

Cancel the common factor of $6$ and $9$ .

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Step 4.3.3.1.1.1

Factor $3$ out of $6$ .

$x = \frac{3 (2)}{9 r} + \frac{72 r}{9 r}$

Step 4.3.3.1.1.2

Cancel the common factors.

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Step 4.3.3.1.1.2.1

Factor $3$ out of $9 r$ .

$x = \frac{3 (2)}{3 (3 r)} + \frac{72 r}{9 r}$

Step 4.3.3.1.1.2.2

Cancel the common factor.

$x = \frac{3 \cdot 2}{3 (3 r)} + \frac{72 r}{9 r}$

Step 4.3.3.1.1.2.3

Rewrite the expression.

$x = \frac{2}{3 r} + \frac{72 r}{9 r}$

Step 4.3.3.1.2

Cancel the common factor of $72$ and $9$ .

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Step 4.3.3.1.2.1

Factor $9$ out of $72 r$ .

$x = \frac{2}{3 r} + \frac{9 (8 r)}{9 r}$

Step 4.3.3.1.2.2

Cancel the common factors.

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Step 4.3.3.1.2.2.1

Factor $9$ out of $9 r$ .

$x = \frac{2}{3 r} + \frac{9 (8 r)}{9 (r)}$

Step 4.3.3.1.2.2.2

Cancel the common factor.

$x = \frac{2}{3 r} + \frac{9 (8 r)}{9 r}$

Step 4.3.3.1.2.2.3

Rewrite the expression.

$x = \frac{2}{3 r} + \frac{8 r}{r}$

Step 4.3.3.1.3

Cancel the common factor of $r$ .

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Step 4.3.3.1.3.1

Cancel the common factor.

$x = \frac{2}{3 r} + \frac{8 r}{r}$

Step 4.3.3.1.3.2

Divide $8$ by $1$ .

$x = \frac{2}{3 r} + 8$