Solve 5x+7/4-3x+5/8=4x+9/5-x-9/3

$$\frac{ 5x+7 }{ 4 } - \frac{ 3x+5 }{ 8 } = \frac{ 4x+9 }{ 5 } - \frac{ x-9 }{ 3 }$$

Solve for x

$$x=9$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120, the least common multiple of 4,8,5,3.

$$30\left(5x+7\right)-15\left(3x+5\right)=24\left(4x+9\right)-40\left(x-9\right)$$

Use the distributive property to multiply 30 by 5x+7.

$$150x+210-15\left(3x+5\right)=24\left(4x+9\right)-40\left(x-9\right)$$

Use the distributive property to multiply -15 by 3x+5.

$$150x+210-45x-75=24\left(4x+9\right)-40\left(x-9\right)$$

Combine 150x and -45x to get 105x.

$$105x+210-75=24\left(4x+9\right)-40\left(x-9\right)$$

Subtract 75 from 210 to get 135.

$$105x+135=24\left(4x+9\right)-40\left(x-9\right)$$

Use the distributive property to multiply 24 by 4x+9.

$$105x+135=96x+216-40\left(x-9\right)$$

Use the distributive property to multiply -40 by x-9.

$$105x+135=96x+216-40x+360$$

Combine 96x and -40x to get 56x.

$$105x+135=56x+216+360$$

Add 216 and 360 to get 576.

$$105x+135=56x+576$$

Subtract 56x from both sides.

$$105x+135-56x=576$$

Combine 105x and -56x to get 49x.

$$49x+135=576$$

Subtract 135 from both sides.

$$49x=576-135$$

Subtract 135 from 576 to get 441.

$$49x=441$$

Divide both sides by 49.

$$x=\frac{441}{49}$$

Divide 441 by 49 to get 9.

$$x=9$$