Finite Math Examples

$18 (\frac{1}{3} x + \frac{1}{6} x) = 18 \cdot 1$

Step 1

Simplify.

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Step 1.1

Simplify each term.

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Step 1.1.1

Combine $\frac{1}{3}$ and $x$ .

$18 (\frac{x}{3} + \frac{1}{6} x) = 18 \cdot 1$

Step 1.1.2

Combine $\frac{1}{6}$ and $x$ .

$18 (\frac{x}{3} + \frac{x}{6}) = 18 \cdot 1$

Step 1.2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$18 (\frac{x}{3} \cdot \frac{2}{2} + \frac{x}{6}) = 18 \cdot 1$

Step 1.3

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{x}{3}$ by $\frac{2}{2}$ .

$18 (\frac{x \cdot 2}{3 \cdot 2} + \frac{x}{6}) = 18 \cdot 1$

Step 1.3.2

Multiply $3$ by $2$ .

$18 (\frac{x \cdot 2}{6} + \frac{x}{6}) = 18 \cdot 1$

Step 1.4

Combine the numerators over the common denominator.

$18 \frac{x \cdot 2 + x}{6} = 18 \cdot 1$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Move $2$ to the left of $x$ .

$18 \frac{2 \cdot x + x}{6} = 18 \cdot 1$

Step 1.5.2

Add $2 x$ and $x$ .

$18 \frac{3 x}{6} = 18 \cdot 1$

Step 1.6

Cancel the common factor of $6$ .

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Step 1.6.1

Factor $6$ out of $18$ .

$6 (3) \frac{3 x}{6} = 18 \cdot 1$

Step 1.6.2

Cancel the common factor.

$6 \cdot 3 \frac{3 x}{6} = 18 \cdot 1$

Step 1.6.3

Rewrite the expression.

$3 (3 x) = 18 \cdot 1$

Step 1.7

Multiply $3$ by $3$ .

$9 x = 18 \cdot 1$

Step 1.8

Multiply $18$ by $1$ .

$9 x = 18$

Step 2

Divide each term in $9 x = 18$ by $9$ and simplify.

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Step 2.1

Divide each term in $9 x = 18$ by $9$ .

$\frac{9 x}{9} = \frac{18}{9}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{9 x}{9} = \frac{18}{9}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{18}{9}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $18$ by $9$ .

$x = 2$