Question

How do you solve `-4(3x+2)=16`?

Answer 1

See a solution process below:

Explanation:

First, divide each side of the equation by `color(red)(-4)` to eliminate the need for parenthesis while keeping the equation balanced:

`(-4(3x + 2))/color(red)(-4) = 16/color(red)(-4)`

`(color(red)(cancel(color(black)(-4)))(3x + 2))/cancel(color(red)(-4)) = -4`

`3x + 2 = -4`

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

`3x + 2 - color(red)(2) = -4 - color(red)(2)`

`3x + 0 = -6`

`3x = -6`

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

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

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

`x = -2`

Answer 2

`x=-2`

Explanation:

`"distribute the bracket"`

`-12x-8=16`

`"add 8 to both sides"`

`-12x=16+8=24`

`"divide both sides by "-12`

`(cancel(-12) x)/cancel(-12)=24/(-12)rArrx=-2`

`color(blue)"As a check"`

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

`-4(-6+2)=-4xx-4=16`

`x=-2" is the solution"`