Question
Solve the following equation and verify your answer:
$\frac{6}{2\text{x}-(3-4\text{x})}=\frac{2}{3}$
$\frac{6}{2\text{x}-(3-4\text{x})}=\frac{2}{3}$
✓
Answer
$\frac{6}{2\text{x}-(3-4\text{x})}=\frac{2}{3}$ $\Rightarrow\frac{6}{2\text{x}-3+4\text{x}}=\frac{2}{3}$$\Rightarrow\frac{6}{6\text{x}-3}=\frac{2}{3}$
By cross multiplication:
$2(6\text{x}-3)=6\times3$ $\Rightarrow12\text{x}=24$ $\Rightarrow\text{x}=\frac{24}{12}=2$ $\therefore\text{x}=2$Verification:
$\text{L.H.S.}=\frac{6}{2\text{x}-(3-4\text{x})}=\frac{6}{2\times2-(3-4\times2)}$ $=\frac{6}{4-(3-8)}=\frac{6}{4+5}=\frac{6}{9}$ $=\frac{2}{3}=\text{R.H.S.}$
By cross multiplication:
$2(6\text{x}-3)=6\times3$ $\Rightarrow12\text{x}=24$ $\Rightarrow\text{x}=\frac{24}{12}=2$ $\therefore\text{x}=2$Verification:
$\text{L.H.S.}=\frac{6}{2\text{x}-(3-4\text{x})}=\frac{6}{2\times2-(3-4\times2)}$ $=\frac{6}{4-(3-8)}=\frac{6}{4+5}=\frac{6}{9}$ $=\frac{2}{3}=\text{R.H.S.}$
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