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

Jun 26, 2015

$- 7 < p < - \frac{1}{2}$

#### Explanation:

Part 1: $4 p < - 2$
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
$\textcolor{w h i t e}{\text{XXXX}}$$p < - \frac{1}{2}$

Part 2: $2 + p \succ 5$
An inequality remains valid if you subtract the same amount from both sides.

Subtracting $2$ from both sides gives
$\textcolor{w h i t e}{\text{XXXX}}$$p > - 7$

Part 3: Combining with "and"
Inequalities connected with the word "and" must both be true .
$\textcolor{w h i t e}{\text{XXXX}}$$p < - \frac{1}{2} \mathmr{and} p > - 7$
$\textcolor{w h i t e}{\text{XXXX}}$or (equivalently)
$\textcolor{w h i t e}{\text{XXXX}}$$- 7 < p < - \frac{1}{2}$