Question

How do you solve `1/2m - 3/4n = 16`, when `n=8`?

Answer 1

See the entire solution process below:

Explanation:

First, substitute `color(red)(8)` for `color(red)(n)` in the equation from the problem:

`1/2m - 3/4color(red)(n) = 16` becomes:

`1/2m - (3/4 xx color(red)(8)) = 16`

First, simplify the term within parenthesis:

`1/2m - (3/color(red)(cancel(color(black)(4))) xx cancel(color(red)(8))2) = 16`

`1/2m - (3 xx 2) = 16`

`1/2m - 6 = 16`

Next, add `color(red)(6)` to each side of the equation to isolate the `m` term while keeping the equation balanced:

`1/2m - 6 + color(red)(6) = 16 + color(red)(6)`

`1/2m - 0 = 22`

`1/2m = 22`

Now, multiply each side of the equation by `color(red)(2)` to solve for `m` while keeping the equation balanced:

`color(red)(2) xx 1/2m = color(red)(2) xx 22`

`cancel(color(red)(2)) xx 1/color(red)(cancel(color(black)(2)))m = 44`

`1m = 44`

`m = 44`