Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Add $\frac{1}{3}$ to both sides of the equation.

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 2.3

Add $2$ and $1$ .

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

Step 2.4

Divide $3$ by $3$ .

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

Step 3

Multiply both sides of the equation by $2$ .

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

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

Step 4.1.1.2

Rewrite the expression.

$x = 2 \cdot 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $2$ by $1$ .

$x = 2$