Finite Math Examples

$\frac{2}{11 x} + \frac{1}{4} = \frac{81}{2 x} - \frac{1}{3}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{81}{2 x}$ from both sides of the equation.

$\frac{2}{11 x} + \frac{1}{4} - \frac{81}{2 x} = - \frac{1}{3}$

Step 1.2

Add $\frac{1}{3}$ to both sides of the equation.

$\frac{2}{11 x} + \frac{1}{4} - \frac{81}{2 x} + \frac{1}{3} = 0$

Step 2

Simplify $\frac{2}{11 x} + \frac{1}{4} - \frac{81}{2 x} + \frac{1}{3}$ .

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Step 2.1

To write $\frac{2}{11 x}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{11 x} \cdot \frac{2}{2} - \frac{81}{2 x} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.2

To write $- \frac{81}{2 x}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$\frac{2}{11 x} \cdot \frac{2}{2} - \frac{81}{2 x} \cdot \frac{11}{11} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.3

Write each expression with a common denominator of $22 x$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{2}{11 x}$ by $\frac{2}{2}$ .

$\frac{2 \cdot 2}{11 x \cdot 2} - \frac{81}{2 x} \cdot \frac{11}{11} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.3.2

Multiply $2$ by $11$ .

$\frac{2 \cdot 2}{22 x} - \frac{81}{2 x} \cdot \frac{11}{11} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.3.3

Multiply $\frac{81}{2 x}$ by $\frac{11}{11}$ .

$\frac{2 \cdot 2}{22 x} - \frac{81 \cdot 11}{2 x \cdot 11} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.3.4

Multiply $11$ by $2$ .

$\frac{2 \cdot 2}{22 x} - \frac{81 \cdot 11}{22 x} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{2 \cdot 2 - 81 \cdot 11}{22 x} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $2$ by $2$ .

$\frac{4 - 81 \cdot 11}{22 x} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.5.2

Multiply $- 81$ by $11$ .

$\frac{4 - 891}{22 x} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.5.3

Subtract $891$ from $4$ .

$\frac{- 887}{22 x} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.6

Move the negative in front of the fraction.

$- \frac{887}{22 x} + \frac{1}{4} + \frac{1}{3} = 0$

Step 2.7

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{887}{22 x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} = 0$

Step 2.8

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{887}{22 x} + \frac{1}{4} \cdot \frac{3}{3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Step 2.9

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.9.1

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$- \frac{887}{22 x} + \frac{3}{4 \cdot 3} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Step 2.9.2

Multiply $4$ by $3$ .

$- \frac{887}{22 x} + \frac{3}{12} + \frac{1}{3} \cdot \frac{4}{4} = 0$

Step 2.9.3

Multiply $\frac{1}{3}$ by $\frac{4}{4}$ .

$- \frac{887}{22 x} + \frac{3}{12} + \frac{4}{3 \cdot 4} = 0$

Step 2.9.4

Multiply $3$ by $4$ .

$- \frac{887}{22 x} + \frac{3}{12} + \frac{4}{12} = 0$

Step 2.10

Combine the numerators over the common denominator.

$- \frac{887}{22 x} + \frac{3 + 4}{12} = 0$

Step 2.11

Add $3$ and $4$ .

$- \frac{887}{22 x} + \frac{7}{12} = 0$