Question

How do you solve `4 (5x + 7) - 3x= 3(4x - 9)`?

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 of the parenthesis:

`color(red)(4)(5x + 7) - 3x = color(blue)(3)(4x - 9)`

`(color(red)(4) xx 5x) + (color(red)(4) xx 7) - 3x = (color(blue)(3) xx 4x) - (color(blue)(3) xx 9)`

`20x + 28 - 3x = 12x - 27`

`20x - 3x + 28 = 12x - 27`

`17x + 28 = 12x - 27`

Next, subtract `color(red)(28)` and `color(blue)(12x)` from each side of the equation to isolate the `x` terms while keeping the equation balanced:

`17x + 28 - color(red)(28) - color(blue)(12x) = 12x - 27 - color(red)(28) - color(blue)(12x)`

`17x - color(blue)(12x) + 28 - color(red)(28) = 12x - color(blue)(12x) - 27 - color(red)(28)`

`5x + 0 = 0 - 55`

`5x = -55`

Now, divide each side of the equation by `color(red)(5)` to solve for `x` while keeping the equation balanced:

`(5x)/color(red)(5) = -55/color(red)(5)`

`(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = -11`

`x = -11`