Solve for x (5x)/4-1/5=1-2/5(x-1/10)

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{2}{5} (x - \frac{1}{10})$

Simplify $1 - \frac{2}{5} \cdot (x - \frac{1}{10})$ .

Simplify each term.

Apply the distributive property.

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{2}{5} x - \frac{2}{5} (- \frac{1}{10})$

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

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} - \frac{2}{5} (- \frac{1}{10})$

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{2}{5}$ into the numerator.

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{- 2}{5} (- \frac{1}{10})$

Move the leading negative in $- \frac{1}{10}$ into the numerator.

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{- 2}{5} \cdot \frac{- 1}{10}$

Factor $2$ out of $- 2$ .

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{2 (- 1)}{5} \cdot \frac{- 1}{10}$

Factor $2$ out of $10$ .

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{2 \cdot - 1}{5} \cdot \frac{- 1}{2 \cdot 5}$

Cancel the common factor.

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{2 \cdot - 1}{5} \cdot \frac{- 1}{2 \cdot 5}$

Rewrite the expression.

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{- 1}{5} \cdot \frac{- 1}{5}$

Multiply $\frac{- 1}{5}$ by $\frac{- 1}{5}$ .

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{- - 1}{5 \cdot 5}$

Multiply $- 1$ by $- 1$ .

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{1}{5 \cdot 5}$

Multiply $5$ by $5$ .

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{x \cdot 2}{5} + \frac{1}{25}$

Move $2$ to the left of $x$ .

$\frac{5 x}{4} - \frac{1}{5} = 1 - \frac{2 x}{5} + \frac{1}{25}$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$\frac{5 x}{4} - \frac{1}{5} = - \frac{2 x}{5} + \frac{25}{25} + \frac{1}{25}$

Combine the numerators over the common denominator.

$\frac{5 x}{4} - \frac{1}{5} = - \frac{2 x}{5} + \frac{25 + 1}{25}$

Add $25$ and $1$ .

$\frac{5 x}{4} - \frac{1}{5} = - \frac{2 x}{5} + \frac{26}{25}$

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

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

$\frac{5 x}{4} - \frac{1}{5} + \frac{2 x}{5} = \frac{26}{25}$

To write $\frac{5 x}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{5 x}{4} \cdot \frac{5}{5} + \frac{2 x}{5} - \frac{1}{5} = \frac{26}{25}$

To write $\frac{2 x}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 x}{4} \cdot \frac{5}{5} + \frac{2 x}{5} \cdot \frac{4}{4} - \frac{1}{5} = \frac{26}{25}$

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 x}{4}$ by $\frac{5}{5}$ .

$\frac{5 x \cdot 5}{4 \cdot 5} + \frac{2 x}{5} \cdot \frac{4}{4} - \frac{1}{5} = \frac{26}{25}$

Multiply $4$ by $5$ .

$\frac{5 x \cdot 5}{20} + \frac{2 x}{5} \cdot \frac{4}{4} - \frac{1}{5} = \frac{26}{25}$

Multiply $\frac{2 x}{5}$ by $\frac{4}{4}$ .

$\frac{5 x \cdot 5}{20} + \frac{2 x \cdot 4}{5 \cdot 4} - \frac{1}{5} = \frac{26}{25}$

Multiply $5$ by $4$ .

$\frac{5 x \cdot 5}{20} + \frac{2 x \cdot 4}{20} - \frac{1}{5} = \frac{26}{25}$

Combine the numerators over the common denominator.

$\frac{5 x \cdot 5 + 2 x \cdot 4}{20} - \frac{1}{5} = \frac{26}{25}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $5 x \cdot 5 + 2 x \cdot 4$ .

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

$\frac{x (5 \cdot 5) + 2 x \cdot 4}{20} - \frac{1}{5} = \frac{26}{25}$

Factor $x$ out of $2 x \cdot 4$ .

$\frac{x (5 \cdot 5) + x (2 \cdot 4)}{20} - \frac{1}{5} = \frac{26}{25}$

Factor $x$ out of $x (5 \cdot 5) + x (2 \cdot 4)$ .

$\frac{x (5 \cdot 5 + 2 \cdot 4)}{20} - \frac{1}{5} = \frac{26}{25}$

Multiply $5$ by $5$ .

$\frac{x (25 + 2 \cdot 4)}{20} - \frac{1}{5} = \frac{26}{25}$

Multiply $2$ by $4$ .

$\frac{x (25 + 8)}{20} - \frac{1}{5} = \frac{26}{25}$

Add $25$ and $8$ .

$\frac{x \cdot 33}{20} - \frac{1}{5} = \frac{26}{25}$

Move $33$ to the left of $x$ .

$\frac{33 x}{20} - \frac{1}{5} = \frac{26}{25}$

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

Add $\frac{1}{5}$ to both sides of the equation.

$\frac{33 x}{20} = \frac{26}{25} + \frac{1}{5}$

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{33 x}{20} = \frac{26}{25} + \frac{1}{5} \cdot \frac{5}{5}$

Write each expression with a common denominator of $25$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{33 x}{20} = \frac{26}{25} + \frac{5}{5 \cdot 5}$

Multiply $5$ by $5$ .

$\frac{33 x}{20} = \frac{26}{25} + \frac{5}{25}$

Combine the numerators over the common denominator.

$\frac{33 x}{20} = \frac{26 + 5}{25}$

Add $26$ and $5$ .

$\frac{33 x}{20} = \frac{31}{25}$

Multiply both sides of the equation by $\frac{20}{33}$ .

$\frac{20}{33} \cdot \frac{33 x}{20} = \frac{20}{33} \cdot \frac{31}{25}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{20}{33} \cdot \frac{33 x}{20}$ .

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20}{33} \cdot \frac{33 x}{20} = \frac{20}{33} \cdot \frac{31}{25}$

Rewrite the expression.

$\frac{1}{33} (33 x) = \frac{20}{33} \cdot \frac{31}{25}$

Cancel the common factor of $33$ .

Factor $33$ out of $33 x$ .

$\frac{1}{33} (33 (x)) = \frac{20}{33} \cdot \frac{31}{25}$

Cancel the common factor.

$\frac{1}{33} (33 x) = \frac{20}{33} \cdot \frac{31}{25}$

Rewrite the expression.

$x = \frac{20}{33} \cdot \frac{31}{25}$

Simplify the right side.

Simplify $\frac{20}{33} \cdot \frac{31}{25}$ .

Cancel the common factor of $5$ .

Factor $5$ out of $20$ .

$x = \frac{5 (4)}{33} \cdot \frac{31}{25}$

Factor $5$ out of $25$ .

$x = \frac{5 \cdot 4}{33} \cdot \frac{31}{5 \cdot 5}$

Cancel the common factor.

$x = \frac{5 \cdot 4}{33} \cdot \frac{31}{5 \cdot 5}$

Rewrite the expression.

$x = \frac{4}{33} \cdot \frac{31}{5}$

Multiply $\frac{4}{33}$ by $\frac{31}{5}$ .

$x = \frac{4 \cdot 31}{33 \cdot 5}$

Multiply.

Multiply $4$ by $31$ .

$x = \frac{124}{33 \cdot 5}$

Multiply $33$ by $5$ .

$x = \frac{124}{165}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{124}{165}$

Decimal Form:

$x = 0.7\overline{51}$

Solve for x (5x)/4-1/5=1-2/5(x-1/10)

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