Solve 4(13-x)=4(x/5+7)-3(4x-20)

$$4 ( 13 - x ) = 4 ( \frac { x } { 5 } + 7 ) - 3 ( 4 x - 20 )$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 5.

$$20\left(13-x\right)=20\left(\frac{x}{5}+7\right)-15\left(4x-20\right)$$

Use the distributive property to multiply 20 by 13-x.

$$260-20x=20\left(\frac{x}{5}+7\right)-15\left(4x-20\right)$$

Use the distributive property to multiply 20 by \frac{x}{5}+7.

$$260-20x=20\times \frac{x}{5}+140-15\left(4x-20\right)$$

Cancel out 5, the greatest common factor in 20 and 5.

$$260-20x=4x+140-15\left(4x-20\right)$$

Use the distributive property to multiply -15 by 4x-20.

$$260-20x=4x+140-60x+300$$

Combine 4x and -60x to get -56x.

$$260-20x=-56x+140+300$$

Add 140 and 300 to get 440.

$$260-20x=-56x+440$$

Add 56x to both sides.

$$260-20x+56x=440$$

Combine -20x and 56x to get 36x.

$$260+36x=440$$

Subtract 260 from both sides.

$$36x=440-260$$

Subtract 260 from 440 to get 180.

$$36x=180$$

Divide both sides by 36.

$$x=\frac{180}{36}$$

Divide 180 by 36 to get 5.

$$x=5$$