Pre-Algebra Examples

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

Step 1

Simplify $\frac{2}{3} x$ .

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

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

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

Step 2

Combine $\frac{1}{15}$ and $x$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

To write $\frac{2 x}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

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 $\frac{2 x}{3}$ by $\frac{5}{5}$ .

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

Step 3.3.2

Multiply $3$ by $5$ .

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

Step 3.4

Combine the numerators over the common denominator.

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

Step 3.5

Simplify the numerator.

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Step 3.5.1

Factor $x$ out of $2 x \cdot 5 - x$ .

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Step 3.5.1.1

Factor $x$ out of $2 x \cdot 5$ .

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

Step 3.5.1.2

Factor $x$ out of $- x$ .

$\frac{x (2 \cdot 5) + x \cdot - 1}{15} = \frac{3}{5}$

Step 3.5.1.3

Factor $x$ out of $x (2 \cdot 5) + x \cdot - 1$ .

$\frac{x (2 \cdot 5 - 1)}{15} = \frac{3}{5}$

Step 3.5.2

Multiply $2$ by $5$ .

$\frac{x (10 - 1)}{15} = \frac{3}{5}$

Step 3.5.3

Subtract $1$ from $10$ .

$\frac{x \cdot 9}{15} = \frac{3}{5}$

Step 3.6

Cancel the common factor of $9$ and $15$ .

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Step 3.6.1

Factor $3$ out of $x \cdot 9$ .

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

Step 3.6.2

Cancel the common factors.

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Step 3.6.2.1

Factor $3$ out of $15$ .

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

Step 3.6.2.2

Cancel the common factor.

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

Step 3.6.2.3

Rewrite the expression.

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

Step 3.7

Move $3$ to the left of $x$ .

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

Step 4

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

$3 x = 3$

Step 5

Divide each term in $3 x = 3$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 x = 3$ by $3$ .

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

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

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

Step 5.2.1.2

Divide $x$ by $1$ .

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

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $3$ by $3$ .

$x = 1$