Testing

1) $$\begin{aligned}
& A=\{(x-2, x+3): x \in \mathbb{Z}\} \\
& B=\{(-x, x+3): x \in \mathbb{Z}\} \\
& C=\{(-x, 7-x): x \in \mathbb{Z}\} \\
& (y, z) \in A \cap B \\
& (t, w) \in B \cap C \\
& \Rightarrow y-z+t+w=?
\end{aligned}$$

2) $$(x-2)\left(1-\frac{4}{x+2}\right)\left(3+\frac{12}{x-2}\right)=?$$

3) $$\left.\begin{array}{l}
(\sqrt{2}-1) x-y=1 \\
2 x-(1+\sqrt{2}) y=4+\sqrt{2}
\end{array}\right\} \Rightarrow x=?$$

4) $$\frac{5^{3} \cdot 5^{5} \cdot 5^{7} \ldots \cdot 5^{221}}{5^{2} \cdot 5^{4} \cdot 5^{6} \ldots \ldots .5^{220}}=?$$

5) $$2 x=3 y=\frac{z}{6}$$

$$z-y-x=\frac{62}{3} \quad \Rightarrow \quad z=?$$

6) $$\frac{y}{2 x-1}=\frac{x}{2 z+3}=\frac{z}{2 y+5}=\frac{1}{3}$$

$$\Rightarrow z+y+x= ?$$

7) $$\left.\begin{array}{l}\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=\frac{3}{4} \\ 3 b+2 d-f=36 \\ 3 a+2 c=35\end{array}\right\} \Rightarrow e=?$$

8) $$7^{x-1}=3 \quad \Rightarrow \quad(189)^{\frac{x}{3 x-2}}=?$$

9) $$f(x+2)-f(x+1)-2 f(x)=0$$

$$\left.\begin{array}{l}f(0)=2 \\ f(1)=3\end{array}\right\} \Rightarrow f(4)= ?$$

10)

$$
f(5)=?
$$