Question

Solve the following equations and verify your answer :

$\frac{3x+5}{2x+7}=4$

Answer 1

$\frac{3x+5}{2x+7}=4$

By cross multiplication :

$4(2x+7)=1\times (3x+5)$

$8x+28=3x+5$

$8x-3x=5-28$ (By transposition)

$\Rightarrow 5x=-23\Rightarrow x=\frac{-23}{5}$

$=x=\frac{-23}{5}$

Verification :

$L.H.S.=\frac{3x+5}{2x+7}=\frac{3\left(\frac{-23}{5}\right)+5}{2\frac{-23}{5})+7}=\frac{\frac{-69}{5}}{\frac{-46}{5}+7}=\frac{\frac{-69+25}{5}}{\frac{-46+35}{5}}=\frac{\frac{-44}{5}}{\frac{-11}{5}}=\frac{-44}{5}\times \frac{-5}{11}=4=R.H.S.$