Algebra Examples

$\frac{5 x}{6} - \frac{1}{2} = \frac{1}{3}$

Step 1

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

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Step 1.1

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{5 x}{6} = \frac{1}{3} + \frac{1}{2}$

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{5 x}{6} = \frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2}$

Step 1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 x}{6} = \frac{1}{3} \cdot \frac{2}{2} + \frac{1}{2} \cdot \frac{3}{3}$

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

$\frac{5 x}{6} = \frac{2}{3 \cdot 2} + \frac{1}{2} \cdot \frac{3}{3}$

Step 1.4.2

Multiply $3$ by $2$ .

$\frac{5 x}{6} = \frac{2}{6} + \frac{1}{2} \cdot \frac{3}{3}$

Step 1.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{5 x}{6} = \frac{2}{6} + \frac{3}{2 \cdot 3}$

Step 1.4.4

Multiply $2$ by $3$ .

$\frac{5 x}{6} = \frac{2}{6} + \frac{3}{6}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{5 x}{6} = \frac{2 + 3}{6}$

Step 1.6

Add $2$ and $3$ .

$\frac{5 x}{6} = \frac{5}{6}$

Step 2

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

$5 x = 5$

Step 3

Divide each term in $5 x = 5$ by $5$ and simplify.

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Step 3.1

Divide each term in $5 x = 5$ by $5$ .

$\frac{5 x}{5} = \frac{5}{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{5}{5}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $5$ by $5$ .

$x = 1$