Question

How do you solve 4p<-2 and 2+p>-5?

Answer 1

`-7< p < -1/2`

Explanation:

Part 1: `4p<-2`
An inequality remains valid if you divide both sides by the same amount provided that amount is greater than zero.

Dividing both sides by `4` gives
`color(white)("XXXX")` `p < -1/2`

Part 2: `2+p>-5`
An inequality remains valid if you subtract the same amount from both sides.

Subtracting `2` from both sides gives
`color(white)("XXXX")` `p> -7`

Part 3: Combining with "and"
Inequalities connected with the word "and" must both be true .
`color(white)("XXXX")` `p < -1/2 and p > -7`
`color(white)("XXXX")`or (equivalently)
`color(white)("XXXX")` `-7 < p < -1/2`