Finite Math Examples

$\frac{x}{15} + \frac{5 x}{6} = \frac{x}{18}$

Step 1

Multiply both sides by $18$ .

$(\frac{x}{15} + \frac{5 x}{6}) \cdot 18 = \frac{x}{18} \cdot 18$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $(\frac{x}{15} + \frac{5 x}{6}) \cdot 18$ .

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Step 2.1.1.1

To write $\frac{x}{15}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$(\frac{x}{15} \cdot \frac{2}{2} + \frac{5 x}{6}) \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.2

To write $\frac{5 x}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{x}{15} \cdot \frac{2}{2} + \frac{5 x}{6} \cdot \frac{5}{5}) \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.1.1.3.1

Multiply $\frac{x}{15}$ by $\frac{2}{2}$ .

$(\frac{x \cdot 2}{15 \cdot 2} + \frac{5 x}{6} \cdot \frac{5}{5}) \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.3.2

Multiply $15$ by $2$ .

$(\frac{x \cdot 2}{30} + \frac{5 x}{6} \cdot \frac{5}{5}) \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.3.3

Multiply $\frac{5 x}{6}$ by $\frac{5}{5}$ .

$(\frac{x \cdot 2}{30} + \frac{5 x \cdot 5}{6 \cdot 5}) \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.3.4

Multiply $6$ by $5$ .

$(\frac{x \cdot 2}{30} + \frac{5 x \cdot 5}{30}) \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + 5 x \cdot 5}{30} \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.5

Simplify the numerator.

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Step 2.1.1.5.1

Factor $x$ out of $x \cdot 2 + 5 x \cdot 5$ .

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Step 2.1.1.5.1.1

Factor $x$ out of $x \cdot 2$ .

$\frac{x (2) + 5 x \cdot 5}{30} \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.5.1.2

Factor $x$ out of $5 x \cdot 5$ .

$\frac{x (2) + x (5 \cdot 5)}{30} \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.5.1.3

Factor $x$ out of $x (2) + x (5 \cdot 5)$ .

$\frac{x (2 + 5 \cdot 5)}{30} \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.5.2

Multiply $5$ by $5$ .

$\frac{x (2 + 25)}{30} \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.5.3

Add $2$ and $25$ .

$\frac{x \cdot 27}{30} \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.6

Simplify terms.

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Step 2.1.1.6.1

Cancel the common factor of $6$ .

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Step 2.1.1.6.1.1

Factor $6$ out of $30$ .

$\frac{x \cdot 27}{6 (5)} \cdot 18 = \frac{x}{18} \cdot 18$

Step 2.1.1.6.1.2

Factor $6$ out of $18$ .

$\frac{x \cdot 27}{6 \cdot 5} \cdot (6 \cdot 3) = \frac{x}{18} \cdot 18$

Step 2.1.1.6.1.3

Cancel the common factor.

$\frac{x \cdot 27}{6 \cdot 5} \cdot (6 \cdot 3) = \frac{x}{18} \cdot 18$

Step 2.1.1.6.1.4

Rewrite the expression.

$\frac{x \cdot 27}{5} \cdot 3 = \frac{x}{18} \cdot 18$

Step 2.1.1.6.2

Combine $\frac{x \cdot 27}{5}$ and $3$ .

$\frac{x \cdot 27 \cdot 3}{5} = \frac{x}{18} \cdot 18$

Step 2.1.1.6.3

Simplify the expression.

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Step 2.1.1.6.3.1

Multiply $3$ by $27$ .

$\frac{x \cdot 81}{5} = \frac{x}{18} \cdot 18$

Step 2.1.1.6.3.2

Move $81$ to the left of $x$ .

$\frac{81 x}{5} = \frac{x}{18} \cdot 18$

Step 2.2

Simplify the right side.

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Step 2.2.1

Cancel the common factor of $18$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{81 x}{5} = \frac{x}{18} \cdot 18$

Step 2.2.1.2

Rewrite the expression.

$\frac{81 x}{5} = x$

Step 3

Solve for $x$ .

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Step 3.1

Multiply both sides by $5$ .

$\frac{81 x}{5} \cdot 5 = x \cdot 5$

Step 3.2

Simplify.

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Step 3.2.1

Simplify the left side.

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Step 3.2.1.1

Cancel the common factor of $5$ .

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Step 3.2.1.1.1

Cancel the common factor.

$\frac{81 x}{5} \cdot 5 = x \cdot 5$

Step 3.2.1.1.2

Rewrite the expression.

$81 x = x \cdot 5$

Step 3.2.2

Simplify the right side.

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Step 3.2.2.1

Move $5$ to the left of $x$ .

$81 x = 5 x$

Step 3.3

Solve for $x$ .

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Step 3.3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.3.1.1

Subtract $5 x$ from both sides of the equation.

$81 x - 5 x = 0$

Step 3.3.1.2

Subtract $5 x$ from $81 x$ .

$76 x = 0$

Step 3.3.2

Divide each term in $76 x = 0$ by $76$ and simplify.

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Step 3.3.2.1

Divide each term in $76 x = 0$ by $76$ .

$\frac{76 x}{76} = \frac{0}{76}$

Step 3.3.2.2

Simplify the left side.

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Step 3.3.2.2.1

Cancel the common factor of $76$ .

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Step 3.3.2.2.1.1

Cancel the common factor.

$\frac{76 x}{76} = \frac{0}{76}$

Step 3.3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{76}$

Step 3.3.2.3

Simplify the right side.

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Step 3.3.2.3.1

Divide $0$ by $76$ .

$x = 0$