Finite Math Examples

$\frac{1}{9} \cdot \frac{x \cdot 2}{3} = 1 - \frac{x}{2}$

Step 1

Simplify $\frac{1}{9} \cdot \frac{x \cdot 2}{3}$ .

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Step 1.1

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

$\frac{1}{9} \cdot \frac{2 \cdot x}{3} = 1 - \frac{x}{2}$

Step 1.2

Multiply $\frac{1}{9} \cdot \frac{2 x}{3}$ .

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Step 1.2.1

Multiply $\frac{1}{9}$ by $\frac{2 x}{3}$ .

$\frac{2 x}{9 \cdot 3} = 1 - \frac{x}{2}$

Step 1.2.2

Multiply $9$ by $3$ .

$\frac{2 x}{27} = 1 - \frac{x}{2}$

Step 2

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

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Step 2.1

Add $\frac{x}{2}$ to both sides of the equation.

$\frac{2 x}{27} + \frac{x}{2} = 1$

Step 2.2

To write $\frac{2 x}{27}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2 x}{27} \cdot \frac{2}{2} + \frac{x}{2} = 1$

Step 2.3

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$\frac{2 x}{27} \cdot \frac{2}{2} + \frac{x}{2} \cdot \frac{27}{27} = 1$

Step 2.4

Write each expression with a common denominator of $54$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{2 x}{27}$ by $\frac{2}{2}$ .

$\frac{2 x \cdot 2}{27 \cdot 2} + \frac{x}{2} \cdot \frac{27}{27} = 1$

Step 2.4.2

Multiply $27$ by $2$ .

$\frac{2 x \cdot 2}{54} + \frac{x}{2} \cdot \frac{27}{27} = 1$

Step 2.4.3

Multiply $\frac{x}{2}$ by $\frac{27}{27}$ .

$\frac{2 x \cdot 2}{54} + \frac{x \cdot 27}{2 \cdot 27} = 1$

Step 2.4.4

Multiply $2$ by $27$ .

$\frac{2 x \cdot 2}{54} + \frac{x \cdot 27}{54} = 1$

Step 2.5

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 + x \cdot 27}{54} = 1$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Factor $x$ out of $2 x \cdot 2 + x \cdot 27$ .

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Step 2.6.1.1

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

$\frac{x (2 \cdot 2) + x \cdot 27}{54} = 1$

Step 2.6.1.2

Factor $x$ out of $x \cdot 27$ .

$\frac{x (2 \cdot 2) + x (27)}{54} = 1$

Step 2.6.1.3

Factor $x$ out of $x (2 \cdot 2) + x (27)$ .

$\frac{x (2 \cdot 2 + 27)}{54} = 1$

Step 2.6.2

Multiply $2$ by $2$ .

$\frac{x (4 + 27)}{54} = 1$

Step 2.6.3

Add $4$ and $27$ .

$\frac{x \cdot 31}{54} = 1$

Step 2.7

Move $31$ to the left of $x$ .

$\frac{31 x}{54} = 1$

Step 3

Multiply both sides of the equation by $\frac{54}{31}$ .

$\frac{54}{31} \cdot \frac{31 x}{54} = \frac{54}{31} \cdot 1$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{54}{31} \cdot \frac{31 x}{54}$ .

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Step 4.1.1.1

Cancel the common factor of $54$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{54}{31} \cdot \frac{31 x}{54} = \frac{54}{31} \cdot 1$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{31} (31 x) = \frac{54}{31} \cdot 1$

Step 4.1.1.2

Cancel the common factor of $31$ .

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Step 4.1.1.2.1

Factor $31$ out of $31 x$ .

$\frac{1}{31} (31 (x)) = \frac{54}{31} \cdot 1$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{31} (31 x) = \frac{54}{31} \cdot 1$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{54}{31} \cdot 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $\frac{54}{31}$ by $1$ .

$x = \frac{54}{31}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{54}{31}$

Decimal Form:

$x = 1.74193548 \dots$

Mixed Number Form:

$x = 1 \frac{23}{31}$