Algebra Examples

$x - 4 \frac{2}{3} = \frac{1}{3}$

Step 1

Simplify the left side.

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Step 1.1

Convert $4 \frac{2}{3}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$x - (4 + \frac{2}{3}) = \frac{1}{3}$

Step 1.1.2

Add $4$ and $\frac{2}{3}$ .

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Step 1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x - (4 \cdot \frac{3}{3} + \frac{2}{3}) = \frac{1}{3}$

Step 1.1.2.2

Combine $4$ and $\frac{3}{3}$ .

$x - (\frac{4 \cdot 3}{3} + \frac{2}{3}) = \frac{1}{3}$

Step 1.1.2.3

Combine the numerators over the common denominator.

$x - \frac{4 \cdot 3 + 2}{3} = \frac{1}{3}$

Step 1.1.2.4

Simplify the numerator.

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Step 1.1.2.4.1

Multiply $4$ by $3$ .

$x - \frac{12 + 2}{3} = \frac{1}{3}$

Step 1.1.2.4.2

Add $12$ and $2$ .

$x - \frac{14}{3} = \frac{1}{3}$

Step 2

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

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Step 2.1

Add $\frac{14}{3}$ to both sides of the equation.

$x = \frac{1}{3} + \frac{14}{3}$

Step 2.2

Combine the numerators over the common denominator.

$x = \frac{1 + 14}{3}$

Step 2.3

Add $1$ and $14$ .

$x = \frac{15}{3}$

Step 2.4

Divide $15$ by $3$ .

$x = 5$