Solve 1-x/5+x+1/4=3x/20+1

$$\frac { 1 - x } { 5 } + \frac { x + 1 } { 4 } = \frac { 3 x } { 20 } + 1$$

Solve for x

$$x = -\frac{11}{2} = -5\frac{1}{2} = -5.5$$

Steps for Solving Linear Equation

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

$$4\left(1-x\right)+5\left(x+1\right)=3x+20$$

Use the distributive property to multiply 4 by 1-x.

$$4-4x+5\left(x+1\right)=3x+20$$

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

$$4-4x+5x+5=3x+20$$

Combine -4x and 5x to get x.

$$4+x+5=3x+20$$

Add 4 and 5 to get 9.

$$9+x=3x+20$$

Subtract 3x from both sides.

$$9+x-3x=20$$

Combine x and -3x to get -2x.

$$9-2x=20$$

Subtract 9 from both sides.

$$-2x=20-9$$

Subtract 9 from 20 to get 11.

$$-2x=11$$

Divide both sides by -2.

$$x=\frac{11}{-2}$$

Fraction \frac{11}{-2} can be rewritten as -\frac{11}{2} by extracting the negative sign.

$$x=-\frac{11}{2}$$