Algebra Examples

$\frac{1}{5} (x - 2) = \frac{1}{10} (x + 6)$

Step 1

Simplify $\frac{1}{5} \cdot (x - 2)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{5} \cdot (x - 2) = \frac{1}{10} \cdot (x + 6)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{5} \cdot (x - 2) = \frac{1}{10} \cdot (x + 6)$

Step 1.3

Apply the distributive property.

$\frac{1}{5} x + \frac{1}{5} \cdot - 2 = \frac{1}{10} \cdot (x + 6)$

Step 1.4

Combine $\frac{1}{5}$ and $x$ .

$\frac{x}{5} + \frac{1}{5} \cdot - 2 = \frac{1}{10} \cdot (x + 6)$

Step 1.5

Combine $\frac{1}{5}$ and $- 2$ .

$\frac{x}{5} + \frac{- 2}{5} = \frac{1}{10} \cdot (x + 6)$

Step 1.6

Move the negative in front of the fraction.

$\frac{x}{5} - \frac{2}{5} = \frac{1}{10} \cdot (x + 6)$

Step 2

Simplify $\frac{1}{10} \cdot (x + 6)$ .

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Step 2.1

Apply the distributive property.

$\frac{x}{5} - \frac{2}{5} = \frac{1}{10} x + \frac{1}{10} \cdot 6$

Step 2.2

Combine $\frac{1}{10}$ and $x$ .

$\frac{x}{5} - \frac{2}{5} = \frac{x}{10} + \frac{1}{10} \cdot 6$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $10$ .

$\frac{x}{5} - \frac{2}{5} = \frac{x}{10} + \frac{1}{2 (5)} \cdot 6$

Step 2.3.2

Factor $2$ out of $6$ .

$\frac{x}{5} - \frac{2}{5} = \frac{x}{10} + \frac{1}{2 \cdot 5} \cdot (2 \cdot 3)$

Step 2.3.3

Cancel the common factor.

$\frac{x}{5} - \frac{2}{5} = \frac{x}{10} + \frac{1}{2 \cdot 5} \cdot (2 \cdot 3)$

Step 2.3.4

Rewrite the expression.

$\frac{x}{5} - \frac{2}{5} = \frac{x}{10} + \frac{1}{5} \cdot 3$

Step 2.4

Combine $\frac{1}{5}$ and $3$ .

$\frac{x}{5} - \frac{2}{5} = \frac{x}{10} + \frac{3}{5}$

Step 3

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

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Step 3.1

Subtract $\frac{x}{10}$ from both sides of the equation.

$\frac{x}{5} - \frac{2}{5} - \frac{x}{10} = \frac{3}{5}$

Step 3.2

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

$\frac{x}{5} \cdot \frac{2}{2} - \frac{x}{10} - \frac{2}{5} = \frac{3}{5}$

Step 3.3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.3.1

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

$\frac{x \cdot 2}{5 \cdot 2} - \frac{x}{10} - \frac{2}{5} = \frac{3}{5}$

Step 3.3.2

Multiply $5$ by $2$ .

$\frac{x \cdot 2}{10} - \frac{x}{10} - \frac{2}{5} = \frac{3}{5}$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - x}{10} - \frac{2}{5} = \frac{3}{5}$

Step 3.5

Subtract $x$ from $x \cdot 2$ .

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Step 3.5.1

Reorder $x$ and $2$ .

$\frac{2 \cdot x - x}{10} - \frac{2}{5} = \frac{3}{5}$

Step 3.5.2

Subtract $x$ from $2 \cdot x$ .

$\frac{x}{10} - \frac{2}{5} = \frac{3}{5}$

Step 4

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

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Step 4.1

Add $\frac{2}{5}$ to both sides of the equation.

$\frac{x}{10} = \frac{3}{5} + \frac{2}{5}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{x}{10} = \frac{3 + 2}{5}$

Step 4.3

Add $3$ and $2$ .

$\frac{x}{10} = \frac{5}{5}$

Step 4.4

Divide $5$ by $5$ .

$\frac{x}{10} = 1$

Step 5

Multiply both sides of the equation by $10$ .

$10 \frac{x}{10} = 10 \cdot 1$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Cancel the common factor of $10$ .

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Step 6.1.1.1

Cancel the common factor.

$10 \frac{x}{10} = 10 \cdot 1$

Step 6.1.1.2

Rewrite the expression.

$x = 10 \cdot 1$

Step 6.2

Simplify the right side.

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Step 6.2.1

Multiply $10$ by $1$ .

$x = 10$