Question:

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

Solution:

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

or $3 \mathrm{x}+5=8 \mathrm{x}+28$

or $8 \mathrm{x}+28=3 \mathrm{x}+5$ (After cross multipl ication)

or $8 \mathrm{x}-3 \mathrm{x}=5-28$

or $5 \mathrm{x}=-23$

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

$\therefore \mathrm{x}=\frac{-23}{5}$ is the solution of given equation.

Check:

Substituting $\mathrm{x}=\frac{-23}{5}$ in the given equation, we get:

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

R.H.S. $=4$

$\therefore \mathrm{L} . \mathrm{H} . \mathrm{S} .=\mathrm{R} . \mathrm{H} . \mathrm{S} .$ for $\mathrm{x}=\frac{-23}{5}$