The given expression is
[tex]20-2p>-2(p+2)+4p[/tex]
First, we use the distributive property on the right side
[tex]20-2p>-2p-4+4p[/tex]
Then, we combine like terms on the right side
[tex]20-2p>2p-4[/tex]
Now, we subtract 2p from each side
[tex]\begin{gathered} 20-2p-2p>2p-2p-4 \\ 20-4p>-4 \end{gathered}[/tex]
Let's subtract 20 from each side now
[tex]\begin{gathered} 20-20-4p>-4-20 \\ -4p>-24 \end{gathered}[/tex]
At last, we divide the inequality by -4
[tex]\begin{gathered} \frac{-4p}{-4}<\frac{-24}{-4} \\ p<6 \end{gathered}[/tex]
It's important to know that the inequality sign changes when we multiply the expression by a negative number.
The image below shows the solution graphically.
