Pre-Algebra Examples

$\frac{1}{3} x = \frac{8}{15} x + \frac{2}{5}$

Step 1

Simplify $\frac{1}{3} x$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{3} x = \frac{8}{15} x + \frac{2}{5}$

Step 1.2

Simplify by adding zeros.

$\frac{1}{3} x = \frac{8}{15} x + \frac{2}{5}$

Step 1.3

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

$\frac{x}{3} = \frac{8}{15} x + \frac{2}{5}$

Step 2

Combine $\frac{8}{15}$ and $x$ .

$\frac{x}{3} = \frac{8 x}{15} + \frac{2}{5}$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Subtract $\frac{8 x}{15}$ from both sides of the equation.

$\frac{x}{3} - \frac{8 x}{15} = \frac{2}{5}$

Step 3.2

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x}{3} \cdot \frac{5}{5} - \frac{8 x}{15} = \frac{2}{5}$

Step 3.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

Multiply $\frac{x}{3}$ by $\frac{5}{5}$ .

$\frac{x \cdot 5}{3 \cdot 5} - \frac{8 x}{15} = \frac{2}{5}$

Step 3.3.2

Multiply $3$ by $5$ .

$\frac{x \cdot 5}{15} - \frac{8 x}{15} = \frac{2}{5}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x \cdot 5 - 8 x}{15} = \frac{2}{5}$

Step 3.5

Simplify the numerator.

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Step 3.5.1

Move $5$ to the left of $x$ .

$\frac{5 \cdot x - 8 x}{15} = \frac{2}{5}$

Step 3.5.2

Subtract $8 x$ from $5 x$ .

$\frac{- 3 x}{15} = \frac{2}{5}$

Step 3.6

Cancel the common factor of $- 3$ and $15$ .

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Step 3.6.1

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x)}{15} = \frac{2}{5}$

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $3$ out of $15$ .

$\frac{3 (- x)}{3 (5)} = \frac{2}{5}$

Step 3.6.2.2

Cancel the common factor.

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

Step 3.6.2.3

Rewrite the expression.

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

Step 3.7

Move the negative in front of the fraction.

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

Step 4

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

$- x = 2$

Step 5

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

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Step 5.1

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

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Dividing two negative values results in a positive value.

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

Step 5.2.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $2$ by $- 1$ .

$x = - 2$