Question

How do you solve `\frac { 1- x } { 3} = \frac { x } { 2} - \frac { x + 1} { 6}`?

Answer 1

`x=3/4`

Explanation:

`(1-x)/3=x/2-(x+1)/6`

We first multiply all terms by the LCM of the denominators to remove the fractions. The LCM is `6`.

`[6xx(1-x)/3]=[6xxx/2]-[6xx(x+1)/6]`

`[2cancel6xx(1-x)/(1cancel3)]=[3cancel6xxx/(1cancel2)]-[1cancel6xx(x+1)/(1cancel6)]`

`2(1-x)=3x-(x+1)`

Simplify both sides. On the right side, the opening of the bracket will convert the plus sign to a minus sign since the product of a positive and a negative is a negative.

`2-2x=3x-x-1`

`2-2x=2x-1`

Add `1` to both sides.

`2-2x+1=2x-1+1`

`3-2x=2x`

Add `2x` to both sides.

`3-2x+2x=2x+2x`

`3=4x`

Divide both sides by `4`.

`3/4=(4x)/4`

`3/4=(1cancel4x)/(1cancel4)`

`3/4=x` or `x=3/4`