Question

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

Answer 1

`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.