Question

Solve the following equation:
$\frac{z}{2}+\frac{z}{3}-\frac{z}{6}=8$

Answer 1

Given:

$\frac{z}{2}+\frac{z}{3}-\frac{z}{6}=8$

To find L.C.M:

$\begin{array}{cc}3& 2,3,6\\ 2& 2,1,2\\ & 1,1,1\end{array}$
L.C.M of $2,3,6$ is $3\times 2=6$

$\frac{z}{2}+\frac{z}{3}-\frac{z}{6}=8$

$\Rightarrow \frac{3z+2z-z}{6}=8$
$\Rightarrow \frac{4z}{6}=8$
$\Rightarrow z=\frac{6\times 8}{4}$
$\Rightarrow z=6\times 2$
$\therefore z=12$