Solve: 4- 2(z-4) 3 =1 2 (2z+5) - Vidyadip

Question

Solve: $4-\frac{2(\text{z}-4)}{3}=\frac{1}{2}(2\text{z}+5)$

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Answer

$4-\frac{2(\text{z}-4)}{3}=\frac{1}{2}(2\text{z}+5)$
$\Rightarrow\frac{12-2(\text{z}-4)}{3}=\frac{1(2\text{z}+5)}{2}$
$\text{(L.C.M of 1 and 3 is 3)}$
$\Rightarrow\frac{12-2\text{z}+8}{3}=\frac{2\text{z}+5}{2}$
$\Rightarrow\frac{20-2\text{z}}{3}=\frac{2\text{z}+5}{2}$
$\Rightarrow2(20-2\text{z})=3(2\text{z}+5)$
$\text{(by cross multiplication)}$
$\Rightarrow40-4\text{z}=6\text{z}+15$
$\Rightarrow40-15=6\text{z}+4\text{z}$
$\Rightarrow25=10\text{z}$
$\Rightarrow10\text{z}=5$
$(\text{by transposition})$
$\Rightarrow\text{z}=\frac{25}{10}=\frac{5}{2}$
$\therefore\text{z}=\frac{5}{2}$

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