How do you solve $5 < \frac{1}{2} p + 3 < 8$ $5<1/2p+3<8$ ?

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Answer 1 · 2017-12-10T21:19:18

$4 < p < 10$ $4 < p < 10$

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

$5 < \frac{1}{2} p + 3$ $5<1/2p+3$
$\Rightarrow 2 < \frac{1}{2} p$ $=>2 < 1/2p$
$\Rightarrow 4 < p$ $=>4 < p$

$\frac{1}{2} p + 3 < 8$ $1/2p+3<8$
$\Rightarrow \frac{1}{2} p < 5$ $=> 1/2p<5$
$\Rightarrow p < 10$ $=> p<10$

put the two together:

$4 < p < 10$ $4 < p < 10$

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