Finite Math Examples

$\frac{1}{3} x + \frac{1}{6} x = 1$

Step 1

Simplify $\frac{1}{3} x + \frac{1}{6} x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$\frac{x}{3} + \frac{1}{6} x = 1$

Step 1.1.2

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

$\frac{x}{3} + \frac{x}{6} = 1$

Step 1.2

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

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

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 $\frac{2}{2}$ .

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

Step 1.3.2

Multiply $3$ by $2$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

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

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

Step 1.5.2

Add $2 x$ and $x$ .

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

Step 1.6

Cancel the common factor of $3$ and $6$ .

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Step 1.6.1

Factor $3$ out of $3 x$ .

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

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $6$ .

$\frac{3 x}{3 \cdot 2} = 1$

Step 1.6.2.2

Cancel the common factor.

$\frac{3 x}{3 \cdot 2} = 1$

Step 1.6.2.3

Rewrite the expression.

$\frac{x}{2} = 1$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 \cdot 1$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 \cdot 1$

Step 3.1.1.2

Rewrite the expression.

$x = 2 \cdot 1$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $2$ by $1$ .

$x = 2$