Algebra Examples

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

Step 1

Multiply both sides of the equation by $2$ .

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

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Cancel the common factor of $2$ .

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Step 2.1.1.1

Cancel the common factor.

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

Step 2.1.1.2

Rewrite the expression.

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

Step 2.2

Simplify the right side.

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Step 2.2.1

Combine $2$ and $\frac{1}{3}$ .

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

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

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

Step 3.2

Write $1$ as a fraction with a common denominator.

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

Step 3.3

Combine the numerators over the common denominator.

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

Step 3.4

Add $2$ and $3$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.\overline{6}$

Mixed Number Form:

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