Question

How do you solve `5u - 7+ 4( 2u + 2) = - 3( u + 3)`?

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:

`5u - 7 + 4(2u + 2) = -3(u + 3)`

`5u - 7 + (4 xx 2u) + (4 xx 2) = (-3 xx u) + (-3 xx 3)`

`5u - 7 + 8u + 8 = -3u - 9`

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

`5u + 8u - 7 + 8 = -3u - 9`

`(5 + 8)u + 1 = -3u - 9`

`13u + 1 = -3u - 9`

Then, subtract `color(red)(1)` and add `color(blue)(3u)` to each side of the equation to isolate the `u` term while keeping the equation balanced:

`13u + 1 - color(red)(1) + color(blue)(3u) = -3u - 9 - color(red)(1) + color(blue)(3u)`

`13u + color(blue)(3u) + 1 - color(red)(1) = -3u + color(blue)(3u) - 9 - color(red)(1)`

`(13 + 3)u + 0 = 0 - 10`

`16u = -10`

Now, divide each side of the equation by `color(red)(16)` to solve for `u` while keeping the equation balanced:

`(16u)/color(red)(16) = -10/color(red)(16)`

`(color(red)(cancel(color(black)(16)))u)/cancel(color(red)(16)) = -(2 xx 5)/color(red)(2 xx 8)`

`u = -(color(red)(cancel(color(black)(2))) xx 5)/color(red)(cancel(2) xx 8)`

`u = -5/8`