[tex]a).\displaystyle \frac{5x-18}{7x+24} = \frac{9}{29} \Rightarrow 29(5x-18)=9(7x+24) \Leftrightarrow \\ \\ \Leftrightarrow 145x-522=63x+216 \Rightarrow 145x-63x=216+522 \Leftrightarrow \\ \\ \Leftrightarrow 82x=738 \Rightarrow x= \frac{738}{82} \Rightarrow x=9[/tex]
[tex]\displaystyle b) \frac{4x+27}{8x+45}= \frac{7}{13} \Rightarrow 13(4x+27)=7(8x+45) \Leftrightarrow \\ \\ \Leftrightarrow 52x+351=56x+315 \Rightarrow 52x-56x=315-351 \Leftrightarrow \\ \\ \Leftrightarrow -4x=-36 \Rightarrow x= \frac{-36}{-4} \Rightarrow x=9[/tex]
[tex]\displaystyle c). \frac{4x-7}{5x-3} = \frac{25}{37} \Rightarrow 37(4x-7)=25(5x-3) \Leftrightarrow \\ \\ \Leftrightarrow 148x-259=125x-75 \Rightarrow 148x-125x=-75+259 \Leftrightarrow \\ \\ \Leftrightarrow 23x=184\Rightarrow x= \frac{184}{23} \Rightarrow x=8[/tex]
[tex]\displaystyle d). \frac{25-7x}{32-5x} = \frac{4}{17} \Rightarrow 17(25-7x)=4(32-5x) \Leftrightarrow \\ \\ \Leftrightarrow 425-119x=128-20x \Rightarrow -119x+20x=128-425 \Leftrightarrow \\ \\ \Leftrightarrow -99x=-297 \Rightarrow x= \frac{-297}{-99} \Rightarrow x=3[/tex]
