Question

Solve the following equations and verify your answer :

$\frac{2x+1}{3x-2}=\frac{5}{9}$

Answer 1

$\frac{2x+1}{3x-2}=\frac{5}{9}$
By cross multiplication :
$9(2x+1)=5(3x-2)$
$\Rightarrow 18x+9=15x-10$
$\Rightarrow 18x-15x=-10-9$ (By transposition)
$\Rightarrow 3x=-19\Rightarrow x=\frac{-19}{3}$
$\therefore x=\frac{-19}{3}$
Verification :
$L.H.S.=\frac{2x+1}{3x-2}=\frac{2\left(\frac{-19}{3}\right)+1}{3\left(\frac{-19}{3}\right)-2}=\frac{\frac{-38}{3}+1}{\frac{-57}{3}-2}=\frac{\frac{-38+3}{3}}{\frac{-57-6}{3}}=\frac{-35}{3}\times \frac{3}{-63}=\frac{5}{9}=R.H.S.$