Question

How do you solve `-7( - 8c + 11) - 20= 19+ 18c + 9c`?

Answer 1

See a solution process below:

Explanation:

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

`color(red)(-7)(-8c + 11) -20 = 19 + 18c + 9c`

`(color(red)(-7) xx -8c) + (color(red)(-7) xx 11) -20 = 19 + 18c + 9c`

`56c + (-77) -20 = 19 + 18c + 9c`

`56c - 77 - 20 = 19 + 18c + 9c`

Next, combine like terms on each side of the equation:

`56c + (-77 - 20) = 19 + (18 + 9)c`

`56c + (-97) = 19 + 27c`

`56c - 97 = 19 + 27c`

Then, add `color(red)(97)` and subtract `color(blue)(27c)` from each side of the equation to isolate the `c` term while keeping the equation balanced:

`56c - 97 + color(red)(97) - color(blue)(27c) = 19 + 27c + color(red)(97) - color(blue)(27c)`

`56c - color(blue)(27c) - 97 + color(red)(97) = 19 + color(red)(97) + 27c - color(blue)(27c)`

`(56 - color(blue)(27))c - 0 = 116 + 0`

`29c = 116`

Now, divide each side of the equation by `color(red)(29)` to solve for `c` while keeping the equation balanced:

`(color(red)(cancel(color(black)(29)))c)/cancel(color(red)(29)) = 4`

`c = 4`