Question

How do you solve `-5p - 14\leq - 2p - p`?

Answer 1

See the entire solution process below:

Explanation:

First combine like terms on the right side of the inequality:

`-5p - 14 <= -2p - 1p`

`-5p - 14 <= (-2 - 1)p`

`-5p - 14 <= -3p`

Next, add `color(red)(5p)` onto each side of the inequality to isolate the `p` term while keeping the inequality balanced:

`color(red)(5p) - 5p - 14 <= color(red)(5p) - 3p`

`0 - 14 <= (color(red)(5) - 3)p`

`-14 <= 2p`

Now, divide each side of the inequality by `color(red)(2)` to solve for `p` while keeping the equation balanced:

`(-14)/color(red)(2) <= 2p/color(red)(2)`

`-7 <= color(red)(cancel(color(black)(2)))p/cancel(color(red)(2))`

`-7 <= p`

To state the solution in terms of `p` we can reverse or "flip" the inequality:

`p >= -7`