Algebra Examples

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

Step 1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2

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

Tap for more steps...

Step 2.1

Subtract $\frac{1}{3}$ from both sides of the equation.

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

Step 2.2

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

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

Step 2.3

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

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

Multiply $3$ by $2$ .

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Subtract $2$ from $5$ .

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

Step 2.6

Cancel the common factor of $3$ and $6$ .

Tap for more steps...

Step 2.6.1

Factor $3$ out of $3$ .

$\frac{x}{2} = \frac{3 (1)}{6}$

Step 2.6.2

Cancel the common factors.

Tap for more steps...

Step 2.6.2.1

Factor $3$ out of $6$ .

$\frac{x}{2} = \frac{3 \cdot 1}{3 \cdot 2}$

Step 2.6.2.2

Cancel the common factor.

$\frac{x}{2} = \frac{3 \cdot 1}{3 \cdot 2}$

Step 2.6.2.3

Rewrite the expression.

$\frac{x}{2} = \frac{1}{2}$

Step 3

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

$x = 1$