Question

How do you solve `4(5k+3)+3(-4k-4)=-48` using the distributive property?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Be careful to manage the signs of the individual terms correctly:

`color(red)(4)(5k + 3) + color(blue)(3)(-4k - 4) = -48` becomes:

`(color(red)(4) xx 5k) + (color(red)(4) xx 3) - (color(blue)(3) xx 4k) - (color(blue)(3) xx 4) = -48`

`20k + 12 - 12k - 12 = -48`

Next, group and combine like terms on the left side of the equation:

`20k - 12k + 12 - 12 = -48`

`(20 - 12)k + 0 = -48`

`8k = -48`

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

`(8k)/color(red)(8) = -48/color(red)(8)`

`(color(red)(cancel(color(black)(8)))k)/cancel(color(red)(8)) = -6`

`k = -6`