Special Symbols

Find the value of the special symbol:

1. If $3+\triangle=7$ what is the value of $\triangle$?
2. If $2(\star + 9)=12$ what is the value of $\star$?
3. If $2\diamond+4 - 3\diamond=2 + \diamond$, what is the value of $\diamond$?
4. If $\dfrac{\circledcirc}{3}-11=\dfrac{1}{2}$ what is the value of $\circledcirc$?
5. If $\dfrac{1}{\square}+8=-10$ what is the value of $\square$?

Using the rules provided by the equation with the special symbols, find the value of the following expressions:

$x\circledS y\circledS z = x+(y)(z)$

6. $3\circledS 4\circledS 5 $
7. $1\circledS 2\circledS 10 $
8. $12\circledS 2\circledS 3 $

$x\spadesuit y\spadesuit z = z(x^y)$

9. $1\spadesuit 2\spadesuit 3$
10. $5\spadesuit 1\spadesuit 8$
11. $3\spadesuit 0\spadesuit 100$

$\dfrac{\heartsuit}{x}=\sqrt{x}+7$

12. $\dfrac{\heartsuit}{4}$
13. $\dfrac{\heartsuit}{64}$
14. $\dfrac{\heartsuit}{10}$