Question

How do you solve and check your solution given `m+7/12=-5/18`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(7/12)` from each side of the equation to solve for `m`:

`m + 7/12 - color(red)(7/12) = - 5/18 - color(red)(7/12)`

`m + 0 = - 5/18 - color(red)(7/12)`

`m = - 5/18 - color(red)(7/12)`

To add/subtract the two factions we need to get them over a common denominator:

`m = - (2/2 xx 5/18) - (3/3 xx color(red)(7/12))`

`m = -10/36 - 21/36`

`m = -31/36`

To check the solution, substitute `-31/36` for `m` in the original equation and calculate the result for both sides of the equation to ensure they are equal:

`m + 7/12 = -5/18` becomes:

`-31/36 + 7/12 = -5/18`

`-31/36 + (3/3 xx 7/12) = -5/18`

`-31/36 + 21/36 = -5/18`

`-10/36 = -5/18`

`-(2 xx 5)/(2 xx 18) = -5/18`

`-(color(red)(cancel(color(black)(2))) xx 5)/(color(red)(cancel(color(black)(2))) xx 18) = -5/18`

`-5/18 = -5/18`

Because both sides of the equation are equal the result checks out.