Precalculus Examples

$\frac{1}{3} x + \frac{1}{4} = 1$

Step 1

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

$\frac{x}{3} + \frac{1}{4} = 1$

Step 2

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

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Step 2.1

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

$\frac{x}{3} = 1 - \frac{1}{4}$

Step 2.2

Write $1$ as a fraction with a common denominator.

$\frac{x}{3} = \frac{4}{4} - \frac{1}{4}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{4 - 1}{4}$

Step 2.4

Subtract $1$ from $4$ .

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

Step 3

Multiply both sides of the equation by $3$ .

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

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

Cancel the common factor of $3$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

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

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

Step 4.2.1.2

Multiply $3$ by $3$ .

$x = \frac{9}{4}$

Step 5