How do you solve #\frac { 2} { 3} x + \frac { 1} { 2} = \frac { 1} { 3} x + 4#?

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Answer 1 · 2017-08-31T09:34:18

#x = 21/2 = 10.5#

First, find the L.C.M of all the Denominators in both R.H.S and L.H.S

#2/3x + 1/2 = 1/3x + 4/1#

#L.C.M = 2 xx 3 = 6#

Multiply through with their L.C.M

#6(2/3x) + 6(1/2) = 6(1/3x) + 6(4/1)#

Simplifying...

#cancel6^2(2/cancel3x) + cancel6^3(1/cancel2) = cancel6^2(1/cancel3x) + 6 xx 4#

# 2 xx 2x + 3 xx 1 =2 xx x + 6 xx 4#

Further Simplifying...

#4x + 3 = 2x + 24#

Collect like terms

#4x - 2x = 24 - 3#

#2x = 21#

#x = 21/2 = 10.5#