Question
Solve the following equation and also check your result in case: $\frac{3\text{a}-2}{3}=\frac{2\text{a}+3}{2}=\text{a}+\frac{7}{6}$
✓
Answer
$\frac{3\text{a}-2}{3}=\frac{2\text{a}+3}{2}=\text{a}+\frac{7}{6}$
$\frac{6\text{a}-4+6\text{a}+9}{6}=\text{a}+\frac{7}{6}$
$12\text{a}+5 =6\text{a}+7$
$6\text{a}=7-5$
$\text{a}=\frac{2}{6}=\frac{1}{3}$
Check: $\text{L.H.S.}=\frac{3\times\frac{1}{3}-2}{3}+=\frac{3\times\frac{1}{3}+3}{2}$
$=\frac{-1}{3}+\frac{11}{6}=\frac{9}{6}=\frac{3}{2}$
$\text{R.H.S.}=\frac{1}{3}+\frac{7}{6}=\frac{9}{6}=\frac{3}{2}$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for a}=\frac{1}{3}$
$\frac{6\text{a}-4+6\text{a}+9}{6}=\text{a}+\frac{7}{6}$
$12\text{a}+5 =6\text{a}+7$
$6\text{a}=7-5$
$\text{a}=\frac{2}{6}=\frac{1}{3}$
Check: $\text{L.H.S.}=\frac{3\times\frac{1}{3}-2}{3}+=\frac{3\times\frac{1}{3}+3}{2}$
$=\frac{-1}{3}+\frac{11}{6}=\frac{9}{6}=\frac{3}{2}$
$\text{R.H.S.}=\frac{1}{3}+\frac{7}{6}=\frac{9}{6}=\frac{3}{2}$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for a}=\frac{1}{3}$
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