Algebra Examples

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

Step 1

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

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Step 1.1

Add $\frac{x}{4}$ to both sides of the equation.

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Multiply $3$ by $4$ .

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

Step 1.4.3

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

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

Step 1.4.4

Multiply $4$ by $3$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Reorder $x$ and $3$ .

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

Step 1.7

Add $4 \cdot x$ and $3 \cdot x$ .

$\frac{7 x}{12} - \frac{1}{4} = \frac{1}{3}$

Step 2

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

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Step 2.1

Add $\frac{1}{4}$ to both sides of the equation.

$\frac{7 x}{12} = \frac{1}{3} + \frac{1}{4}$

Step 2.2

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

$\frac{7 x}{12} = \frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4}$

Step 2.3

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

$\frac{7 x}{12} = \frac{1}{3} \cdot \frac{4}{4} + \frac{1}{4} \cdot \frac{3}{3}$

Step 2.4

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

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Step 2.4.1

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

$\frac{7 x}{12} = \frac{4}{3 \cdot 4} + \frac{1}{4} \cdot \frac{3}{3}$

Step 2.4.2

Multiply $3$ by $4$ .

$\frac{7 x}{12} = \frac{4}{12} + \frac{1}{4} \cdot \frac{3}{3}$

Step 2.4.3

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

$\frac{7 x}{12} = \frac{4}{12} + \frac{3}{4 \cdot 3}$

Step 2.4.4

Multiply $4$ by $3$ .

$\frac{7 x}{12} = \frac{4}{12} + \frac{3}{12}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{7 x}{12} = \frac{4 + 3}{12}$

Step 2.6

Add $4$ and $3$ .

$\frac{7 x}{12} = \frac{7}{12}$

Step 3

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

$7 x = 7$

Step 4

Divide each term in $7 x = 7$ by $7$ and simplify.

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Step 4.1

Divide each term in $7 x = 7$ by $7$ .

$\frac{7 x}{7} = \frac{7}{7}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{7}{7}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{7}{7}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $7$ by $7$ .

$x = 1$