Question

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

Answer 1

See a solution process below:

Explanation:

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

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

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

`-12 + (-4x) + 5 = 4x + 12`

`-12 - 4x + 5 = 4x + 12`

`-12 + 5 - 4x = 4x + 12`

`-7 - 4x = 4x + 12`

Next, add `color(red)(4x)` and subtract `color(blue)(12)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`-7 - color(blue)(12) - 4x + color(red)(4x) = 4x + color(red)(4x) + 12 - color(blue)(12)`

`-19 - 0 = (4 + color(red)(4))x + 0`

`-19 = 8x`

Now, divide each side of the equation by `color(red)(8)` to solve for `x` while keeping the equation balanced:

`-19/color(red)(8) = (8x)/color(red)(8)`

`-19/8 = (color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8))`

`-19/8 = x`

`x = -19/8`