1. -3p+7=-3

-3p+7=-3
-3p=-10
-3p/3=-10/3
-p=-10/3 or -p=-3 and 1/3

but it doesn't seem to pass a check

-3(-10/3)+7=17 not -3

What am I doing wrong here?

2. -p=-10/3 then p=10/3
-3(10/3)+7=-10+7=-3

3. 2/3y+2=1/5+y

Doh! Nevermind. I figured it out. A stupid mistake.

2/3y+2=1/5+y
15(2/3y+2)=15(1/5+y)
10y+30=3+15y
10y+30=15y+3
30=5y+3
27=5y
27/5=y

but when I check it

2/3(27/5)+2=1/5+27/5
2/3(27/5)+2=28/5
54/15+2=28/5
84/15=28/5

I know I'm making a stupid mistake somewhere but what is it?

Doh! Nevermind. I figured it out. A stupid mistake.

2/3y+2=1/5+y
15(2/3y+2)=15(1/5+y)
10y+30=3+15y
10y+30=15y+3
30=5y+3
27=5y
27/5=y

but when I check it

2/3(27/5)+2=1/5+27/5
2/3(27/5)+2=28/5
54/15+2=28/5
84/15=28/5

I know I'm making a stupid mistake somewhere but what is it?
your answer $\displaystyle y=\frac{27}{5}$ is actually correct.

$\displaystyle \frac{2}{3}y + 2 = \frac{1}{5} + y$

$\displaystyle \frac{2}{3}*\frac{27}{5} + 2 = \frac{1}{5} + \frac{27}{5}$

$\displaystyle \frac{18}{5} + 2 = \frac{28}{5}$

$\displaystyle \frac{28}{5}=\frac{28}{5}$

$\displaystyle \frac{84}{15}=\frac{28}{5}$

its just the lowest term