Solve for x 5/4(x+1/5)=21/4

$\frac{5}{4} (x + \frac{1}{5}) = \frac{21}{4}$

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} (\frac{5}{4} \cdot (x + \frac{1}{5})) = \frac{4}{5} \cdot \frac{21}{4}$

Simplify both sides of the equation.

Simplify the left side.

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

Apply the distributive property.

$\frac{4}{5} (\frac{5}{4} x + \frac{5}{4} \cdot \frac{1}{5}) = \frac{4}{5} \cdot \frac{21}{4}$

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

$\frac{4}{5} (\frac{5 x}{4} + \frac{5}{4} \cdot \frac{1}{5}) = \frac{4}{5} \cdot \frac{21}{4}$

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{4}{5} (\frac{5 x}{4} + \frac{5}{4} \cdot \frac{1}{5}) = \frac{4}{5} \cdot \frac{21}{4}$

Rewrite the expression.

$\frac{4}{5} (\frac{5 x}{4} + \frac{1}{4}) = \frac{4}{5} \cdot \frac{21}{4}$

Apply the distributive property.

$\frac{4}{5} \cdot \frac{5 x}{4} + \frac{4}{5} \cdot \frac{1}{4} = \frac{4}{5} \cdot \frac{21}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} + \frac{4}{5} \cdot \frac{1}{4} = \frac{4}{5} \cdot \frac{21}{4}$

Rewrite the expression.

$\frac{1}{5} (5 x) + \frac{4}{5} \cdot \frac{1}{4} = \frac{4}{5} \cdot \frac{21}{4}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) + \frac{4}{5} \cdot \frac{1}{4} = \frac{4}{5} \cdot \frac{21}{4}$

Cancel the common factor.

$\frac{1}{5} (5 x) + \frac{4}{5} \cdot \frac{1}{4} = \frac{4}{5} \cdot \frac{21}{4}$

Rewrite the expression.

$x + \frac{4}{5} \cdot \frac{1}{4} = \frac{4}{5} \cdot \frac{21}{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

$x + \frac{4}{5} \cdot \frac{1}{4} = \frac{4}{5} \cdot \frac{21}{4}$

Rewrite the expression.

$x + \frac{1}{5} = \frac{4}{5} \cdot \frac{21}{4}$

Simplify the right side.

Simplify $\frac{4}{5} \cdot \frac{21}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$x + \frac{1}{5} = \frac{4}{5} \cdot \frac{21}{4}$

Rewrite the expression.

$x + \frac{1}{5} = \frac{1}{5} \cdot 21$

Combine $\frac{1}{5}$ and $21$ .

$x + \frac{1}{5} = \frac{21}{5}$

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

Subtract $\frac{1}{5}$ from both sides of the equation.

$x = \frac{21}{5} - \frac{1}{5}$

Combine the numerators over the common denominator.

$x = \frac{21 - 1}{5}$

Subtract $1$ from $21$ .

$x = \frac{20}{5}$

Divide $20$ by $5$ .

$x = 4$

Solve for x 5/4(x+1/5)=21/4

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