How do you solve #\frac { 1} { 3} x + \frac { 5} { 6} = \frac { 1} { 6} x - \frac { 1} { 2}#?

1 Answer
Dec 22, 2016

#color(green)(x=-8)#

Explanation:

Given
#color(white)("XXX")1/3x+5/6=1/6x-1/2#

Noting that the LCM of the denominators: #{3,6,6,2}# is #6#
we can clear the fractions by multiplying everything on both sides by #6#

#color(white)("XXX")2x+5=x-3#

Subtracting #x# from both sides (to eliminate the variable on the right side)
#color(white)("XXX")x+5=-3#

Subtracting #5# from both sides (to eliminate the constant from the left side)
#color(white)("XXX")x=-8#

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It's always a good idea to verify your results.
In this case we could evaluate the Left and Right Sides using #x=-8# to ensure that the results are equal.

#{: ("Left Side",color(white)("XX"),"Right Side"), (1/3x+5/6,,1/6x-1/2), (,"with "x=-8,), (=((-8)/3+5/6),,=(-8)/6-1/2), (=(-16+5)/6,,=(-8-3)/6), (=-11/6,,=-11/6) :}#

Since #LS = RS#, we have verified our results.