How do you solve #3/4 - 2/3>x/6#?

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Answer 1 · 2018-05-26T14:20:16

#x<1/2#

#3/4 - 2/3>x/6#

You can solve this with fractions but I always recommend we turn them into integers to make everything WAY easier:

To do that we need a common denominator of #4, 3 and 6#

prime factors:

#4=2*2#
#3=3#
#6=2*3#

so the common factors in all three terns are: #2*2*3 = 12#

so here is the trick, we multiply 12 by both sides of the inequality like so:

#12(3/4 - 2/3)>12*(x/6)#

remember #12 = 12/1#

#(12/1*3/4) - (12/1*2/3)>(12/1*x/6)#

then cross divide:

#(3/1*3/1) - (4/1*2/1)>(2/1*x/1)#

#(3*3) - (4*2)>(2*x)#

#9 -8>2x#

Now it is super simple to solve:

#9 -8>2x#

#1>2x#

#1/2>x#

#x<1/2#