Solve x+6/4+x-3/5=5x-4/8

$$\frac{ x+6 }{ 4 } + \frac{ x-3 }{ 5 } = \frac{ 5x-4 }{ 8 }$$

Solve for x

$$x=8$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 40, the least common multiple of 4,5,8.

$$10\left(x+6\right)+8\left(x-3\right)=5\left(5x-4\right)$$

Use the distributive property to multiply 10 by x+6.

$$10x+60+8\left(x-3\right)=5\left(5x-4\right)$$

Use the distributive property to multiply 8 by x-3.

$$10x+60+8x-24=5\left(5x-4\right)$$

Combine 10x and 8x to get 18x.

$$18x+60-24=5\left(5x-4\right)$$

Subtract 24 from 60 to get 36.

$$18x+36=5\left(5x-4\right)$$

Use the distributive property to multiply 5 by 5x-4.

$$18x+36=25x-20$$

Subtract 25x from both sides.

$$18x+36-25x=-20$$

Combine 18x and -25x to get -7x.

$$-7x+36=-20$$

Subtract 36 from both sides.

$$-7x=-20-36$$

Subtract 36 from -20 to get -56.

$$-7x=-56$$

Divide both sides by -7.

$$x=\frac{-56}{-7}$$

Divide -56 by -7 to get 8.

$$x=8$$