Solve x-2/5-5-2x/4+4x-1/20=4-x

$$\frac{ x-2 }{ 5 } - \frac{ 5-2x }{ 4 } + \frac{ 4x-1 }{ 20 } =4-x$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 20, the least common multiple of 5,4,20.

$$4\left(x-2\right)-5\left(5-2x\right)+4x-1=80-20x$$

Use the distributive property to multiply 4 by x-2.

$$4x-8-5\left(5-2x\right)+4x-1=80-20x$$

Use the distributive property to multiply -5 by 5-2x.

$$4x-8-25+10x+4x-1=80-20x$$

Subtract 25 from -8 to get -33.

$$4x-33+10x+4x-1=80-20x$$

Combine 4x and 10x to get 14x.

$$14x-33+4x-1=80-20x$$

Combine 14x and 4x to get 18x.

$$18x-33-1=80-20x$$

Subtract 1 from -33 to get -34.

$$18x-34=80-20x$$

Add 20x to both sides.

$$18x-34+20x=80$$

Combine 18x and 20x to get 38x.

$$38x-34=80$$

Add 34 to both sides.

$$38x=80+34$$

Add 80 and 34 to get 114.

$$38x=114$$

Divide both sides by 38.

$$x=\frac{114}{38}$$

Divide 114 by 38 to get 3.

$$x=3$$