Question

How do you solve `6(m - 2) + 14 = 3(m + 2) - 10`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(6)(m -2) + 14 = color(blue)(3)(m + 2) - 10`

`(color(red)(6) xx m) - (color(red)(6) xx 2) + 14 = (color(blue)(3) xx m) + (color(blue)(3) xx 2) - 10`

`6m - 12 + 14 = 3m + 6 - 10`

`6m + 2 = 3m - 4`

Next, subtract `color(red)(2)` and `color(blue)(3m)` from each side of the equation to isolate the `m` term while keeping the equation balanced:

`6m + 2 - color(red)(2) - color(blue)(3m) = 3m - 4 - color(red)(2) - color(blue)(3m)`

`6m - color(blue)(3m) + 2 - color(red)(2) = 3m - color(blue)(3m) - 4 - color(red)(2)`

`(6 - 3)m + 0 = 0 - 6`

`3m = -6`

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

`(3m)/color(red)(3) = -6/color(red)(3)`

`(color(red)(cancel(color(black)(3)))m)/cancel(color(red)(3)) = -2`

`m = -2`