Question

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

Answer 1

$$\begin{gathered} \frac{3\mathrm{a}-2}{3}+\frac{2\mathrm{a}+3}{2}=\mathrm{a}+\frac{7}{6} \\ \mathrm{or}\frac{6\mathrm{a}-4+6\mathrm{a}+9}{6}=\mathrm{a}+\frac{7}{6} \\ \mathrm{or}12\mathrm{a}+5=6\mathrm{a}+7 \\ \mathrm{or}6\mathrm{a}=7-5 \\ \mathrm{or}\mathrm{a}=\frac{2}{6}=\frac{1}{3} \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{3\times {\displaystyle \frac{1}{3}}-2}{3}+\frac{2\times {\displaystyle \frac{1}{3}}+3}{2}=\frac{-1}{3}+\frac{11}{6}=\frac{9}{6}=\frac{3}{2} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{1}{3}+\frac{7}{6}=\frac{9}{6}=\frac{3}{2} \end{gathered}$$

$\therefore$ L.H.S. = R.H.S. for a = $\frac{1}{3}$