Algebra Examples

$\frac{1}{4} (x + \frac{3}{5}) = \frac{2}{5}$

Step 1

Multiply both sides of the equation by $4$ .

$4 (\frac{1}{4} \cdot (x + \frac{3}{5})) = 4 (\frac{2}{5})$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $4 (\frac{1}{4} \cdot (x + \frac{3}{5}))$ .

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Step 2.1.1.1

Apply the distributive property.

$4 (\frac{1}{4} x + \frac{1}{4} \cdot \frac{3}{5}) = 4 (\frac{2}{5})$

Step 2.1.1.2

Combine $\frac{1}{4}$ and $x$ .

$4 (\frac{x}{4} + \frac{1}{4} \cdot \frac{3}{5}) = 4 (\frac{2}{5})$

Step 2.1.1.3

Multiply $\frac{1}{4} \cdot \frac{3}{5}$ .

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Step 2.1.1.3.1

Multiply $\frac{1}{4}$ by $\frac{3}{5}$ .

$4 (\frac{x}{4} + \frac{3}{4 \cdot 5}) = 4 (\frac{2}{5})$

Step 2.1.1.3.2

Multiply $4$ by $5$ .

$4 (\frac{x}{4} + \frac{3}{20}) = 4 (\frac{2}{5})$

Step 2.1.1.4

Apply the distributive property.

$4 \frac{x}{4} + 4 (\frac{3}{20}) = 4 (\frac{2}{5})$

Step 2.1.1.5

Cancel the common factor of $4$ .

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Step 2.1.1.5.1

Cancel the common factor.

$4 \frac{x}{4} + 4 (\frac{3}{20}) = 4 (\frac{2}{5})$

Step 2.1.1.5.2

Rewrite the expression.

$x + 4 (\frac{3}{20}) = 4 (\frac{2}{5})$

Step 2.1.1.6

Cancel the common factor of $4$ .

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Step 2.1.1.6.1

Factor $4$ out of $20$ .

$x + 4 \frac{3}{4 (5)} = 4 (\frac{2}{5})$

Step 2.1.1.6.2

Cancel the common factor.

$x + 4 \frac{3}{4 \cdot 5} = 4 (\frac{2}{5})$

Step 2.1.1.6.3

Rewrite the expression.

$x + \frac{3}{5} = 4 (\frac{2}{5})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $4 (\frac{2}{5})$ .

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Step 2.2.1.1

Combine $4$ and $\frac{2}{5}$ .

$x + \frac{3}{5} = \frac{4 \cdot 2}{5}$

Step 2.2.1.2

Multiply $4$ by $2$ .

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

Step 3

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

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Step 3.1

Subtract $\frac{3}{5}$ from both sides of the equation.

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $3$ from $8$ .

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

Step 3.4

Divide $5$ by $5$ .

$x = 1$