Solve 3x-1/5-5x+1/6=x+1/8-3

$$\frac { 3 x - 1 } { 5 } - \frac { 5 x + 1 } { 6 } = \frac { x + 1 } { 8 } - 3$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 120, the least common multiple of 5,6,8.

$$24\left(3x-1\right)-20\left(5x+1\right)=15\left(x+1\right)-360$$

Use the distributive property to multiply 24 by 3x-1.

$$72x-24-20\left(5x+1\right)=15\left(x+1\right)-360$$

Use the distributive property to multiply -20 by 5x+1.

$$72x-24-100x-20=15\left(x+1\right)-360$$

Combine 72x and -100x to get -28x.

$$-28x-24-20=15\left(x+1\right)-360$$

Subtract 20 from -24 to get -44.

$$-28x-44=15\left(x+1\right)-360$$

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

$$-28x-44=15x+15-360$$

Subtract 360 from 15 to get -345.

$$-28x-44=15x-345$$

Subtract 15x from both sides.

$$-28x-44-15x=-345$$

Combine -28x and -15x to get -43x.

$$-43x-44=-345$$

Add 44 to both sides.

$$-43x=-345+44$$

Add -345 and 44 to get -301.

$$-43x=-301$$

Divide both sides by -43.

$$x=\frac{-301}{-43}$$

Divide -301 by -43 to get 7.

$$x=7$$