Solve 1/1-x/1+1-x/5=1/10x-frac{2}{5}+frac{1}{1}

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

Solve for x

$$x=\frac{6}{13}\approx 0.461538462$$

Steps for Solving Linear Equation

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

$$10-10x+2\left(1-x\right)=1x-4+10$$

Use the distributive property to multiply 2 by 1-x.

$$10-10x+2-2x=1x-4+10$$

Add 10 and 2 to get 12.

$$12-10x-2x=1x-4+10$$

Combine -10x and -2x to get -12x.

$$12-12x=1x-4+10$$

Add -4 and 10 to get 6.

$$12-12x=1x+6$$

Subtract 1x from both sides.

$$12-12x-x=6$$

Combine -12x and -x to get -13x.

$$12-13x=6$$

Subtract 12 from both sides.

$$-13x=6-12$$

Subtract 12 from 6 to get -6.

$$-13x=-6$$

Divide both sides by -13.

$$x=\frac{-6}{-13}$$

Fraction \frac{-6}{-13} can be simplified to \frac{6}{13} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{6}{13}$$