[tex]\it 1)\ 2x+3=-7|_{-3} \Rightarrow 2x=-10 \Rightarrow x=-5\in\mathbb{Z}\\ \\ 2)\ \dfrac{x}{3}=\dfrac{3}{x} \Rightarrow x\cdot x=3\cdot3 \Rightarrow x^2=9 \Rightarrow \sqrt{x^2}=\sqrt9 \Rightarrow |x|=3 \Rightarrow x=\pm3\\ \\ \\ 3)\ |x+2|=4 \Rightarrow x+2=\pm4 \Rightarrow x+2\in\{-4,\ 4\}|_{-2} \Rightarrow x\in\{-6,\ 2\}[/tex]
[tex]\it 4)\ |2x+3|\leq1 \Rightarrow -1\leq2x+3\leq1|_{-3} \Rightarrow -4\leq2x\leq-2|_{:2} \Rightarrow \\ \\ \Rightarrow -2\leq x\leq-1 \stackrel{x\in\mathbb{Z}}{\Longrightarrow}\ x\in\{-2,\ -1\}\\ \\ 5)\ 2(x-2)=3(x+2) \Rightarrow 2x-4=3x+6 \Rightarrow -4-6=3x-2x \Rightarrow\\ \\ \Rightarrow -10=x \Rightarrow x=-10[/tex]
