Question

Solve each of the following equation and also check your result in each case:
$\frac{6x+1}{2}+1=\frac{7x-3}{3}$

Answer 1

$$\begin{gathered} \frac{6\mathrm{x}+1}{2}+1=\frac{7\mathrm{x}-3}{3} \\ \mathrm{or}\frac{6\mathrm{x}+1+2}{2}=\frac{7\mathrm{x}-3}{3} \\ \mathrm{or}18\mathrm{x}+9=14\mathrm{x}-6 \\ \mathrm{or}18\mathrm{x}-14\mathrm{x}=-6-9 \\ \mathrm{or}4\mathrm{x}=-15 \\ \mathrm{or}\mathrm{x}=\frac{-15}{4} \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{6\times {\displaystyle \frac{-15}{4}}+1}{2}+1=\frac{-45+2+4}{4}=\frac{-39}{4} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{7\times {\displaystyle \frac{-15}{4}}-3}{3}=\frac{-105-12}{12}=\frac{-39}{4} \end{gathered}$$

$\therefore$ L.H.S. = R.H.S. for x = $\frac{-15}{4}$