Question

How do you solve `-2( 4p + 6) \geq 5p + 40`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the term in parenthesis on the left side of the inequality by multiplying each term within the parenthesis by the term outside the parenthesis:

`color(red)(-2)(4p + 6) >= 5p + 40`

`(color(red)(-2) * 4p) + (color(red)(-2) * 6) >= 5p + 40`

`-8p + (-12) >= 5p + 40`

`-8p - 12 >= 5p + 40`

Next, add `color(red)(8p)` and subtract `color(blue)(40)` from each side of the inequality to isolate the `p` term while keeping the inequality balanced:

#color(red)(8p) - 8p - 12 - color(blue)(40) >= color(red)(8p) + 5p + 40 - color(blue)(40)#

`0 - 52 >= (color(red)(8) + 5)p + 0`

`-52 >= 13p`

Now, divide each side of the inequality by `color(red)(13)` to solve for `p` while keeping the inequality balanced:

`-52/color(red)(13) >= (13p)/color(red)(13)`

`-4 >= (color(red)(cancel(color(black)(13)))p)/cancel(color(red)(13))`

`-4 >= p`

We can state the solution in terms of `p` by reversing or "flipping" the entire inequality:

`p <= -4`