Solve for x (3x)/4=5x+y-6

$\frac{3 x}{4} = 5 x + y - 6$

Multiply both sides by $4$ .

$\frac{3 x}{4} \cdot 4 = (5 x + y - 6) \cdot 4$

Simplify.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 x}{4} \cdot 4 = (5 x + y - 6) \cdot 4$

Rewrite the expression.

$3 x = (5 x + y - 6) \cdot 4$

Simplify the right side.

Simplify $(5 x + y - 6) \cdot 4$ .

Apply the distributive property.

$3 x = 5 x \cdot 4 + y \cdot 4 - 6 \cdot 4$

Simplify.

Multiply $4$ by $5$ .

$3 x = 20 x + y \cdot 4 - 6 \cdot 4$

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

$3 x = 20 x + 4 \cdot y - 6 \cdot 4$

Multiply $- 6$ by $4$ .

$3 x = 20 x + 4 \cdot y - 24$

$3 x = 20 x + 4 y - 24$

Solve for $x$ .

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

Subtract $20 x$ from both sides of the equation.

$3 x - 20 x = 4 y - 24$

Subtract $20 x$ from $3 x$ .

$- 17 x = 4 y - 24$

Divide each term in $- 17 x = 4 y - 24$ by $- 17$ and simplify.

Divide each term in $- 17 x = 4 y - 24$ by $- 17$ .

$\frac{- 17 x}{- 17} = \frac{4 y}{- 17} + \frac{- 24}{- 17}$

Simplify the left side.

Cancel the common factor of $- 17$ .

Cancel the common factor.

$\frac{- 17 x}{- 17} = \frac{4 y}{- 17} + \frac{- 24}{- 17}$

Divide $x$ by $1$ .

$x = \frac{4 y}{- 17} + \frac{- 24}{- 17}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{4 y}{17} + \frac{- 24}{- 17}$

Dividing two negative values results in a positive value.

$x = - \frac{4 y}{17} + \frac{24}{17}$