Question

How do you solve `(\frac { 5} { 6} - n ) - \frac { 1} { 3} = \frac { 5} { 12}`?

Answer 1

`n = (1)/(12)`

Explanation:

`((5)/(6)−(n)/(1))−(1)/(3)=(5)/(12)`

1) Solve the subtraction inside the parentheses

`(5 - 6n)/(6) - (1)/(3) = (5)/(12)`

2) Clear the fractions by multiplying all the terms on both sides by `12` and letting the denominators cancel
`2 (5 - 6n) - 4 = 5`

3) Clear the parentheses by distributing the `2`
`10 - 12n - 4 = 5`

4) Combine like terms
`6 - 12n = 5`

5) Subtract `6` from both sides to isolate the `-12n` term
`- 12n = - 1`

6) Divide both sides by `-12` to isolate `n`
`n = (1)/(12)` `larr` answer

Check

Sub in `(1)/(12)` in the place of `n` to see if the equation still equals `(5)/(12)`

`((5)/(6)−n) −(1)/(3)=(5)/(12)`

`((5)/(6)−(1)/(12)) −(1)/(3) "should equal" (5)/(12)`

Give each term the common denominator of `12`
`((10)/(12)−(1)/(12)) −(4)/(12) "should equal" (5)/(12)`

Clear the parentheses by solving the subtraction
`(9)/(12) −(4)/(12) "should equal" (5)/(12)`

Combine like terms by doing the subtraction
`(5)/(12) "does equal" (5)/(12)`

`Check`