Question

How do you solve `4(4 - w) = 3(2w + 2)`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parethesis:

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

`(color(red)(4) xx 4) - (color(red)(4) xx w) = (color(blue)(3) xx 2w) + (color(blue)(3) xx 2)`

`16 - 4w = 6w + 6`

Next, add `color(red)(4w)` and subtract `color(blue)(6)` from each side of the equation to isolate the `w` terms while keeping the equation balanced:

`16 - 4w + color(red)(4w) - color(blue)(6) = 6w + 6 + color(red)(4w) - color(blue)(6)`

`16 - color(blue)(6) - 4w + color(red)(4w) = 6w + color(red)(4w) + 6 - color(blue)(6)`

`10 - 0 = (6 + color(red)(4))w + 0`

`10 = 10w`

`10/color(red)(10) = (10w)/color(red)(10)`

`1 = (color(red)(cancel(color(black)(10)))w)/cancel(color(red)(10))`

`1 = w`

`w = 1`