# How do you solve 5<1/2p+3<8?

Dec 10, 2017

$4 < p < 10$

#### Explanation:

Split the equation into 2 parts:
$5 < \frac{1}{2} p + 3$
$\frac{1}{2} p + 3 < 8$

$5 < \frac{1}{2} p + 3$
$\implies 2 < \frac{1}{2} p$
$\implies 4 < p$

$\frac{1}{2} p + 3 < 8$
$\implies \frac{1}{2} p < 5$
$\implies p < 10$

put the two together:

$4 < p < 10$