[tex]\displaystyle a). \frac{17}{233} \cdot x=92 \Rightarrow \frac{17x}{233} =92 \Rightarrow 17x=233 \cdot 92 \Rightarrow 17x=21436 \Leftrightarrow \\ \\ \Leftrightarrow x= \frac{21436}{17} \\ \\ b). \frac{23}{6} \cdot x=54 \Rightarrow \frac{23x}{6} =54 \Rightarrow 23x=6 \cdot 54 \Rightarrow 23x=324 \Rightarrow x= \frac{324}{23} \\ \\ c). \frac{31}{12} \cdot x=96 \Rightarrow \frac{31x}{12} =96 \Rightarrow 31x=12 \cdot 96 \Rightarrow 31x=1152 \Rightarrow x= \frac{1152}{31} [/tex]
[tex]\displaystyle d). \frac{5}{x+2} \cdot (3x+2)=10 \Rightarrow \frac{5(3x+2)}{x+2} =10 \Rightarrow \frac{15x+10}{x+2} =10 \Leftrightarrow \\ \\ \Leftrightarrow 15x+10=10(x+2) \Rightarrow 15x+10=10x+20 \Leftrightarrow \\ \\ \Leftrightarrow 15x-10x=20-10 \Rightarrow 5x=10 \Rightarrow x= \frac{10}{5} \Rightarrow x=2[/tex]
