Question
Solve the following equation for the unknown: $\frac{a-1}{2}-\frac{a+1}{3}=5-a$
✓
Answer
$\frac{a-1}{2}-\frac{a+1}{3}=5-a $
$\Rightarrow \frac{a-1}{2}-\frac{a+1}{3}+a=5$
Take the $\text{LCM}$ of all the denominators, that is, $2$ and $3$ which is $6 .$
Multiply throughout by the $\text{LCM}$
$\Rightarrow 3(a-1)-2(a+1)+6 a=30 $
$\Rightarrow 3 a-3-2 a-2+6 a=30 $
$\Rightarrow 7 a=35 $
$\Rightarrow a=5 .$
$\Rightarrow \frac{a-1}{2}-\frac{a+1}{3}+a=5$
Take the $\text{LCM}$ of all the denominators, that is, $2$ and $3$ which is $6 .$
Multiply throughout by the $\text{LCM}$
$\Rightarrow 3(a-1)-2(a+1)+6 a=30 $
$\Rightarrow 3 a-3-2 a-2+6 a=30 $
$\Rightarrow 7 a=35 $
$\Rightarrow a=5 .$
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