Finite Math Examples

$\frac{3}{8} u + \frac{1}{4} = \frac{1}{4} u + \frac{1}{8}$

Step 1

Combine $\frac{3}{8}$ and $u$ .

$\frac{3 u}{8} + \frac{1}{4} = \frac{1}{4} u + \frac{1}{8}$

Step 2

Combine $\frac{1}{4}$ and $u$ .

$\frac{3 u}{8} + \frac{1}{4} = \frac{u}{4} + \frac{1}{8}$

Step 3

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

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Step 3.1

Subtract $\frac{u}{4}$ from both sides of the equation.

$\frac{3 u}{8} + \frac{1}{4} - \frac{u}{4} = \frac{1}{8}$

Step 3.2

To write $- \frac{u}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{3 u}{8} - \frac{u}{4} \cdot \frac{2}{2} + \frac{1}{4} = \frac{1}{8}$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{u}{4}$ by $\frac{2}{2}$ .

$\frac{3 u}{8} - \frac{u \cdot 2}{4 \cdot 2} + \frac{1}{4} = \frac{1}{8}$

Step 3.3.2

Multiply $4$ by $2$ .

$\frac{3 u}{8} - \frac{u \cdot 2}{8} + \frac{1}{4} = \frac{1}{8}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{3 u - u \cdot 2}{8} + \frac{1}{4} = \frac{1}{8}$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $u$ out of $3 u - u \cdot 2$ .

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Step 3.5.1.1.1

Factor $u$ out of $3 u$ .

$\frac{u \cdot 3 - u \cdot 2}{8} + \frac{1}{4} = \frac{1}{8}$

Step 3.5.1.1.2

Factor $u$ out of $- u \cdot 2$ .

$\frac{u \cdot 3 + u (- 1 \cdot 2)}{8} + \frac{1}{4} = \frac{1}{8}$

Step 3.5.1.1.3

Factor $u$ out of $u \cdot 3 + u (- 1 \cdot 2)$ .

$\frac{u (3 - 1 \cdot 2)}{8} + \frac{1}{4} = \frac{1}{8}$

Step 3.5.1.2

Multiply $- 1$ by $2$ .

$\frac{u (3 - 2)}{8} + \frac{1}{4} = \frac{1}{8}$

Step 3.5.1.3

Subtract $2$ from $3$ .

$\frac{u \cdot 1}{8} + \frac{1}{4} = \frac{1}{8}$

Step 3.5.2

Multiply $u$ by $1$ .

$\frac{u}{8} + \frac{1}{4} = \frac{1}{8}$

Step 4

Move all terms not containing $u$ to the right side of the equation.

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Step 4.1

Subtract $\frac{1}{4}$ from both sides of the equation.

$\frac{u}{8} = \frac{1}{8} - \frac{1}{4}$

Step 4.2

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{u}{8} = \frac{1}{8} - \frac{1}{4} \cdot \frac{2}{2}$

Step 4.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.3.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$\frac{u}{8} = \frac{1}{8} - \frac{2}{4 \cdot 2}$

Step 4.3.2

Multiply $4$ by $2$ .

$\frac{u}{8} = \frac{1}{8} - \frac{2}{8}$

Step 4.4

Combine the numerators over the common denominator.

$\frac{u}{8} = \frac{1 - 2}{8}$

Step 4.5

Subtract $2$ from $1$ .

$\frac{u}{8} = \frac{- 1}{8}$

Step 4.6

Move the negative in front of the fraction.

$\frac{u}{8} = - \frac{1}{8}$

Step 5

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$u = - 1$