Answer
The solutions are $p=10$ and $p=\frac{2}{3}$.
Work Step by Step
The given equation is
$\Rightarrow 4|p-3|=|2p+8|$
Write the two related linear equations.
$4(p-3)=2p+8$ ...... (1)
$4(p-3)=-(2p+8)$ ...... (2)
Solve equation (1).
$\Rightarrow 4(p-3)=2p+8$
Use distributive property.
$\Rightarrow 4p-12=2p+8$
Add $12-2p$ to each side.
$\Rightarrow 4p-12+12-2p=2p+8+12-2p$
Simplify.
$\Rightarrow 2p=20$
Divide each side by $2$.
$\Rightarrow \frac{2p}{2}=\frac{20}{2}$
Simplify.
$\Rightarrow p=10$
Check : $p=10$
$\Rightarrow 4|p-3|=|2p+8|$
$\Rightarrow 4|10-3|=|2(10)+8|$
$\Rightarrow 4|7|=|20+8|$
$\Rightarrow 4(7)=|28|$
$\Rightarrow 28=28$
True.
Solve equation (2).
$\Rightarrow 4(p-3)=-(2p+8)$
Use distributive property.
$\Rightarrow 4p-12=-2p-8$
Add $12+2p$ to each side.
$\Rightarrow 4p-12+12+2p=-2p-8+12+2p$
Simplify.
$\Rightarrow 6p=4$
Divide each side by $6$.
$\Rightarrow \frac{6p}{6}=\frac{4}{6}$
Simplify.
$\Rightarrow p=\frac{2}{3}$
Check : $p=\frac{2}{3}$
$\Rightarrow 4|p-3|=|2p+8|$
$\Rightarrow 4|\frac{2}{3}-3|=|2(\frac{2}{3})+8|$
$\Rightarrow 4|\frac{2-9}{3}|=|\frac{4}{3}+8|$
$\Rightarrow 4|\frac{-7}{3}|=|\frac{4+24}{3}|$
$\Rightarrow 4(\frac{7}{3})=|\frac{28}{3}|$
$\Rightarrow \frac{28}{3}=\frac{28}{3}$
True.
Hence, the solutions are $p=10$ and $p=\frac{2}{3}$.
