Solve 5x+1/6-6x-1/5=3x+1/4-1/1

$$\frac { 5 x + 1 } { 6 } - \frac { 6 x - 1 } { 5 } = \frac { 3 x + 1 } { 4 } - \frac { 1 } { 1 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 6,5,4.

$$10\left(5x+1\right)-12\left(6x-1\right)=15\left(3x+1\right)-60$$

Use the distributive property to multiply 10 by 5x+1.

$$50x+10-12\left(6x-1\right)=15\left(3x+1\right)-60$$

Use the distributive property to multiply -12 by 6x-1.

$$50x+10-72x+12=15\left(3x+1\right)-60$$

Combine 50x and -72x to get -22x.

$$-22x+10+12=15\left(3x+1\right)-60$$

Add 10 and 12 to get 22.

$$-22x+22=15\left(3x+1\right)-60$$

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

$$-22x+22=45x+15-60$$

Subtract 60 from 15 to get -45.

$$-22x+22=45x-45$$

Subtract 45x from both sides.

$$-22x+22-45x=-45$$

Combine -22x and -45x to get -67x.

$$-67x+22=-45$$

Subtract 22 from both sides.

$$-67x=-45-22$$

Subtract 22 from -45 to get -67.

$$-67x=-67$$

Divide both sides by -67.

$$x=\frac{-67}{-67}$$

Divide -67 by -67 to get 1.

$$x=1$$