Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Add $\frac{3}{4}$ to both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Multiply $4$ by $3$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $3$ by $3$ .

$\frac{x}{3} = \frac{- 1 + 9}{12}$

Step 2.5.2

Add $- 1$ and $9$ .

$\frac{x}{3} = \frac{8}{12}$

Step 2.6

Cancel the common factor of $8$ and $12$ .

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Step 2.6.1

Factor $4$ out of $8$ .

$\frac{x}{3} = \frac{4 (2)}{12}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $4$ out of $12$ .

$\frac{x}{3} = \frac{4 \cdot 2}{4 \cdot 3}$

Step 2.6.2.2

Cancel the common factor.

$\frac{x}{3} = \frac{4 \cdot 2}{4 \cdot 3}$

Step 2.6.2.3

Rewrite the expression.

$\frac{x}{3} = \frac{2}{3}$

Step 3

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

$x = 2$