Question

How do you solve `\frac { 1} { 3} + \frac { 1} { 2} n = 4`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the equation by `color(red)(6)` (the least common denominator for the two fractions) to eliminate the fractions while keeping the equation balanced:

`color(red)(6)(1/3 + 1/2n) = color(red)(6) xx 4`

`(color(red)(6) xx 1/3) + (color(red)(6) xx 1/2n) = 24`

`color(red)(6)/3 + color(red)(6)/2n = 24`

`2 + 3n = 24`

Next. subtract `color(red)(2)` from each side of the equation to isolate the `n` term while keeping the equation balanced:

`2 - color(red)(2) + 3n = 24 - color(red)(2)`

`0 + 3n = 22`

`3n = 22`

Now, divide each side of the equation by `color(red)(3)` to solve for `n` while keeping the equation balanced:

`(3n)/color(red)(3) = 22/color(red)(3)`

`(color(red)(cancel(color(black)(3)))n)/cancel(color(red)(3)) = 22/3`

`n = 22/3`