Finite Math Examples

$\frac{x}{3} + \frac{5}{4} = 10$

Step 1

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

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Step 1.1

Subtract $\frac{5}{4}$ from both sides of the equation.

$\frac{x}{3} = 10 - \frac{5}{4}$

Step 1.2

To write $10$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{3} = 10 \cdot \frac{4}{4} - \frac{5}{4}$

Step 1.3

Combine $10$ and $\frac{4}{4}$ .

$\frac{x}{3} = \frac{10 \cdot 4}{4} - \frac{5}{4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{10 \cdot 4 - 5}{4}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $10$ by $4$ .

$\frac{x}{3} = \frac{40 - 5}{4}$

Step 1.5.2

Subtract $5$ from $40$ .

$\frac{x}{3} = \frac{35}{4}$

Step 2

Multiply both sides of the equation by $3$ .

$3 \frac{x}{3} = 3 (\frac{35}{4})$

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 $3$ .

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Step 3.1.1.1

Cancel the common factor.

$3 \frac{x}{3} = 3 (\frac{35}{4})$

Step 3.1.1.2

Rewrite the expression.

$x = 3 (\frac{35}{4})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $3 (\frac{35}{4})$ .

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Step 3.2.1.1

Combine $3$ and $\frac{35}{4}$ .

$x = \frac{3 \cdot 35}{4}$

Step 3.2.1.2

Multiply $3$ by $35$ .

$x = \frac{105}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{105}{4}$

Decimal Form:

$x = 26.25$

Mixed Number Form:

$x = 26 \frac{1}{4}$