Question

How do you solve `5/2w - 1/3 = 5/6w - 1/8`?

Answer 1

`w=color(blue)(1/8)`

Explanation:

The easiest way is to convert all the factions so they have the same denominator.

`LCM(2,3,6,8)=24`

So we will use `24` as our common denominator.

`color(white)("XXX")5/2=(5xx12)/(2xx12)=60/24`

`color(white)("XXX")1/3=(1xx8)/(3xx8)=8/24`

`color(white)("XXX")5/6=(5xx4)/(6xx4)=20/24`

`color(white)("XXX")1/8=(1xx3)/(8xx3)=3/24`

So we can re-write the given equation: `5/2w-1/3=5/6w-1/8` as
`60/24w-8/24=20/24w-3/24`

After multiplying both sides by `24`:
`60w-8=20w-3`

Simplifying
`40w=5`

`w=5/40=1/8`