Solve for x 5/3y-4/5x=1

$\frac{5}{3} y - \frac{4}{5} x = 1$

Step 1

Simplify each term.

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

$\frac{5 y}{3} - \frac{4}{5} x = 1$

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

$\frac{5 y}{3} - \frac{x \cdot 4}{5} = 1$

Move $4$ to the left of $x$ .

$\frac{5 y}{3} - \frac{4 x}{5} = 1$

Step 2

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

$- \frac{4 x}{5} = 1 - \frac{5 y}{3}$

Step 3

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

$- \frac{5}{4} (- \frac{4 x}{5}) = - \frac{5}{4} (1 - \frac{5 y}{3})$

Step 4

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{5}{4} (- \frac{4 x}{5})$ .

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{4}$ into the numerator.

$\frac{- 5}{4} (- \frac{4 x}{5}) = - \frac{5}{4} (1 - \frac{5 y}{3})$

Move the leading negative in $- \frac{4 x}{5}$ into the numerator.

$\frac{- 5}{4} \cdot \frac{- 4 x}{5} = - \frac{5}{4} (1 - \frac{5 y}{3})$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{4} \cdot \frac{- 4 x}{5} = - \frac{5}{4} (1 - \frac{5 y}{3})$

Cancel the common factor.

$\frac{5 \cdot - 1}{4} \cdot \frac{- 4 x}{5} = - \frac{5}{4} (1 - \frac{5 y}{3})$

Rewrite the expression.

$\frac{- 1}{4} (- 4 x) = - \frac{5}{4} (1 - \frac{5 y}{3})$

Cancel the common factor of $4$ .

Factor $4$ out of $- 4 x$ .

$\frac{- 1}{4} (4 (- x)) = - \frac{5}{4} (1 - \frac{5 y}{3})$

Cancel the common factor.

$\frac{- 1}{4} (4 (- x)) = - \frac{5}{4} (1 - \frac{5 y}{3})$

Rewrite the expression.

$- - x = - \frac{5}{4} (1 - \frac{5 y}{3})$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{4} (1 - \frac{5 y}{3})$

Multiply $x$ by $1$ .

$x = - \frac{5}{4} (1 - \frac{5 y}{3})$

Simplify the right side.

Simplify $- \frac{5}{4} (1 - \frac{5 y}{3})$ .

Apply the distributive property.

$x = - \frac{5}{4} \cdot 1 - \frac{5}{4} (- \frac{5 y}{3})$

Multiply $- 1$ by $1$ .

$x = - \frac{5}{4} - \frac{5}{4} (- \frac{5 y}{3})$

Multiply $- \frac{5}{4} (- \frac{5 y}{3})$ .

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

Multiply $5$ by $5$ .

$x = - \frac{5}{4} + \frac{25 y}{4 \cdot 3}$

Multiply $4$ by $3$ .

$x = - \frac{5}{4} + \frac{25 y}{12}$

Step 5

Reorder $- \frac{5}{4}$ and $\frac{25 y}{12}$ .

$x = \frac{25 y}{12} - \frac{5}{4}$

Solve for x 5/3y-4/5x=1

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