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

1 Answer
Alan P.
Jun 23, 2018

#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#

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