Question
Solve the following equations. Check your result in case. $\frac{2\text{x}+5}{3\text{x}+4}=3$
✓
Answer
$\frac{2\text{x}+5}{3\text{x}+4}=3$ (By cross multiplication)
$3(3\text{x}+4)=1(2\text{x}+5)$
$9\text{x}+12=2\text{x}+5$
$\Rightarrow9\text{x}-2\text{x}=5-12$
$\Rightarrow7\text{x}=-7$
$\Rightarrow\text{x}=\frac{-7}{7}=-1$
$\text{x}=-1$
Check: $\text{L.H.S}.=\frac{2\text{x}+5}{3\text{x}+4}=\frac{2(-1)+5}{3(-1)+4}=\frac{-2\ +\ 5}{-3\ +\ 4}$
$=\frac{3}{1}=3=\text{R.H.S.}$ Hence $\text{x}=-1$
$3(3\text{x}+4)=1(2\text{x}+5)$
$9\text{x}+12=2\text{x}+5$
$\Rightarrow9\text{x}-2\text{x}=5-12$
$\Rightarrow7\text{x}=-7$
$\Rightarrow\text{x}=\frac{-7}{7}=-1$
$\text{x}=-1$
Check: $\text{L.H.S}.=\frac{2\text{x}+5}{3\text{x}+4}=\frac{2(-1)+5}{3(-1)+4}=\frac{-2\ +\ 5}{-3\ +\ 4}$
$=\frac{3}{1}=3=\text{R.H.S.}$ Hence $\text{x}=-1$
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