Hello,
We know that if we make the same operation on both sides, we don't affect the equation:
For example:
[tex]2=2 \\ 2\bold{+2}=2\bold{+2} \\ 4=4[/tex]
Do you see? we add 2 on both sides and we don't affect the equality
We can do the same with the multiplication, for example
4=4 (i'll multiply both sides by 1/2)
[tex]4*\bold{ \frac{1}{2}}=4*\bold{ \frac{1}{2}} \\ 2=2[/tex]
Now, we do exactly the same in your excercise:
[tex]P=2(L+W) \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[multiply\,\,by\,\,1/2] \\ \\ P*\bold{ \frac{1}{2}}=2(L+W)*\bold{ \frac{1}{2}} \\ \\ \frac{P}{2}=L+W\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[Subtract\,\,L]\\ \\ \frac{P}{2}-\bold{L}=L+W-\bold{L}\\ \\ \frac{P}{2}-\bold{L}=L-\bold{L}+W \\ \\ \frac{P}{2}-L=W\\ \\ \boxed{ W= \frac{P}{2}-L }[/tex]
