Algebra Examples

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

Step 1

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

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Step 1.1

Subtract $\frac{1}{2}$ from both sides of the equation.

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

Step 1.2

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

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

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 $\frac{3}{3}$ .

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

Step 1.3.2

Multiply $2$ by $3$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Subtract $3$ from $5$ .

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

Step 1.6

Cancel the common factor of $2$ and $6$ .

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Step 1.6.1

Factor $2$ out of $2$ .

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

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $2$ out of $6$ .

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

Step 1.6.2.2

Cancel the common factor.

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

Step 1.6.2.3

Rewrite the expression.

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

Step 2

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

$2 x = 1$

Step 3

Divide each term in $2 x = 1$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 x = 1$ by $2$ .

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

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

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

Step 3.2.1.2

Divide $x$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 0.5$