Solve 3(x-8)/5+7(x+5)/3=4(7x+1.5)/15+1/3

$$\frac{ 3(x-8) }{ 5 } + \frac{ 7(x+5) }{ 3 } = \frac{ 4(7x+1.5) }{ 15 } + \frac{ 1 }{ 3 }$$

Solve for x

$$x=-5.75$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 15, the least common multiple of 5,3,15.

$$3\times 3\left(x-8\right)+5\times 7\left(x+5\right)=4\left(7x+1.5\right)+5$$

Multiply 3 and 3 to get 9.

$$9\left(x-8\right)+5\times 7\left(x+5\right)=4\left(7x+1.5\right)+5$$

Use the distributive property to multiply 9 by x-8.

$$9x-72+5\times 7\left(x+5\right)=4\left(7x+1.5\right)+5$$

Multiply 5 and 7 to get 35.

$$9x-72+35\left(x+5\right)=4\left(7x+1.5\right)+5$$

Use the distributive property to multiply 35 by x+5.

$$9x-72+35x+175=4\left(7x+1.5\right)+5$$

Combine 9x and 35x to get 44x.

$$44x-72+175=4\left(7x+1.5\right)+5$$

Add -72 and 175 to get 103.

$$44x+103=4\left(7x+1.5\right)+5$$

Use the distributive property to multiply 4 by 7x+1.5.

$$44x+103=28x+6+5$$

Add 6 and 5 to get 11.

$$44x+103=28x+11$$

Subtract 28x from both sides.

$$44x+103-28x=11$$

Combine 44x and -28x to get 16x.

$$16x+103=11$$

Subtract 103 from both sides.

$$16x=11-103$$

Subtract 103 from 11 to get -92.

$$16x=-92$$

Divide both sides by 16.

$$x=\frac{-92}{16}$$

Reduce the fraction \frac{-92}{16} to lowest terms by extracting and canceling out 4.

$$x=-\frac{23}{4}$$