# How do you solve and graph -5<3p+7<=22?

Jun 27, 2017

$\textcolor{red}{- 4 < p \le 5}$

#### Explanation:

Remember that you can add or subtract any amount to all components of an inequality without changing the validity or orientation of the inequality.
Therefore
$\textcolor{w h i t e}{\text{XXX}} - 5 < 3 p + 7 < 22$
after subtracting $7$ from all components
$\rightarrow \textcolor{w h i t e}{\text{XX}} - 12 < 3 p \le 15$

Also remember that you can multiply or divide all components of an inequality by any constant greater than zero without changing the validity or orientation of the inequality.
Therefore
$\textcolor{w h i t e}{\text{XXX}} - 12 < 3 p \le 15$
after dividing all components by $3$
$\rightarrow \textcolor{w h i t e}{\text{XX}} - 4 < p \le 5$

Note that in drawing the number line graph for this solution, an open circle is used at $\left(- 4\right)$ to indicate that this value is not included in the solution,
and a closed (or solid) circle is used at $\left(+ 5\right)$ to indicate that this vale is included.