Solve 4/5-x-1/6=x+3/10+2-x/4

$$\frac{ 4 }{ 5 } - \frac{ x-1 }{ 6 } = \frac{ x+3 }{ 10 } + \frac{ 2-x }{ 4 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 60, the least common multiple of 5,6,10,4.

$$48-10\left(x-1\right)=6\left(x+3\right)+15\left(2-x\right)$$

Use the distributive property to multiply -10 by x-1.

$$48-10x+10=6\left(x+3\right)+15\left(2-x\right)$$

Add 48 and 10 to get 58.

$$58-10x=6\left(x+3\right)+15\left(2-x\right)$$

Use the distributive property to multiply 6 by x+3.

$$58-10x=6x+18+15\left(2-x\right)$$

Use the distributive property to multiply 15 by 2-x.

$$58-10x=6x+18+30-15x$$

Add 18 and 30 to get 48.

$$58-10x=6x+48-15x$$

Combine 6x and -15x to get -9x.

$$58-10x=-9x+48$$

Add 9x to both sides.

$$58-10x+9x=48$$

Combine -10x and 9x to get -x.

$$58-x=48$$

Subtract 58 from both sides.

$$-x=48-58$$

Subtract 58 from 48 to get -10.

$$-x=-10$$

Multiply both sides by -1.

$$x=10$$