Algebra Examples

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

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.

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $3$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Add $5$ and $3$ .

$\frac{x}{3} = \frac{8}{6}$

Step 1.6

Cancel the common factor of $8$ and $6$ .

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Step 1.6.1

Factor $2$ out of $8$ .

$\frac{x}{3} = \frac{2 (4)}{6}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $6$ .

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

Step 1.6.2.2

Cancel the common factor.

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

Step 1.6.2.3

Rewrite the expression.

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

Step 2

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

$x = 4$