Solve for x 1/4(x+3/5)=2/5

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Algebra

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

Multiply both sides of the equation by $4$ .

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

Simplify both sides of the equation.

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Simplify the left side.

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

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Apply the distributive property.

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

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

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

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

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

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

Multiply $4$ by $5$ .

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

Apply the distributive property.

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

Cancel the common factor of $4$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $4$ .

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Factor $4$ out of $20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

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

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

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

Multiply $4$ by $2$ .

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

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

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

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

Combine the numerators over the common denominator.

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

Subtract $3$ from $8$ .

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

Divide $5$ by $5$ .

$x = 1$

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