Solve for x 3(x-7)=5(x-1)-4x

$3 (x - 7) = 5 (x - 1) - 4 x$

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$5 (x - 1) - 4 x = 3 (x - 7)$

Simplify $5 (x - 1) - 4 x$ .

Simplify each term.

Apply the distributive property.

$5 x + 5 \cdot - 1 - 4 x = 3 (x - 7)$

Multiply $5$ by $- 1$ .

$5 x - 5 - 4 x = 3 (x - 7)$

Subtract $4 x$ from $5 x$ .

$x - 5 = 3 (x - 7)$

Simplify $3 (x - 7)$ .

Apply the distributive property.

$x - 5 = 3 x + 3 \cdot - 7$

Multiply $3$ by $- 7$ .

$x - 5 = 3 x - 21$

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

Subtract $3 x$ from both sides of the equation.

$x - 5 - 3 x = - 21$

Subtract $3 x$ from $x$ .

$- 2 x - 5 = - 21$

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

Add $5$ to both sides of the equation.

$- 2 x = - 21 + 5$

Add $- 21$ and $5$ .

$- 2 x = - 16$

Divide each term in $- 2 x = - 16$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 16$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 16}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 16}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 2}$

Simplify the right side.

Divide $- 16$ by $- 2$ .

$x = 8$