Solve 4(x-2)/3+3x+1/8=3(6x-5)/5-9

$$\frac { 4 ( x - 2 ) } { 3 } + \frac { 3 x + 1 } { 8 } = \frac { 3 ( 6 x - 5 ) } { 5 } - 9$$

Solve for x

$$x=5$$

Steps for Solving Linear Equation

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

$$40\times 4\left(x-2\right)+15\left(3x+1\right)=24\times 3\left(6x-5\right)-1080$$

Multiply 40 and 4 to get 160.

$$160\left(x-2\right)+15\left(3x+1\right)=24\times 3\left(6x-5\right)-1080$$

Use the distributive property to multiply 160 by x-2.

$$160x-320+15\left(3x+1\right)=24\times 3\left(6x-5\right)-1080$$

Use the distributive property to multiply 15 by 3x+1.

$$160x-320+45x+15=24\times 3\left(6x-5\right)-1080$$

Combine 160x and 45x to get 205x.

$$205x-320+15=24\times 3\left(6x-5\right)-1080$$

Add -320 and 15 to get -305.

$$205x-305=24\times 3\left(6x-5\right)-1080$$

Multiply 24 and 3 to get 72.

$$205x-305=72\left(6x-5\right)-1080$$

Use the distributive property to multiply 72 by 6x-5.

$$205x-305=432x-360-1080$$

Subtract 1080 from -360 to get -1440.

$$205x-305=432x-1440$$

Subtract 432x from both sides.

$$205x-305-432x=-1440$$

Combine 205x and -432x to get -227x.

$$-227x-305=-1440$$

Add 305 to both sides.

$$-227x=-1440+305$$

Add -1440 and 305 to get -1135.

$$-227x=-1135$$

Divide both sides by -227.

$$x=\frac{-1135}{-227}$$

Divide -1135 by -227 to get 5.

$$x=5$$