Question
$\frac{2\text{x}}{3}-\frac{3\text{x}}{8}=\frac{7}{12}$
✓
Answer
$\frac{2\text{x}}{3}-\frac{3\text{x}}{8}=\frac{7}{12}$
$\frac{16\text{x}-9\text{x}}{24}=\frac{7}{12}$ (L.C.M of 3, 8 = 24)
$\frac{7\text{x}}{24}=\frac{7}{12}$
Dividing by $\frac{7}{24}$
$=\frac{7\text{x}}{24}+\frac{7}{24}=\frac{7}{12}+\frac{7}{24}$
$\Rightarrow\frac{7\text{x}}{24}\times\frac{24}{7}=\frac{7}{12}\times\frac{24}{12}$
$\Rightarrow\text{x}=2$
$\therefore\text{x}=2$
Verification:
$\text{L.H.S}$ $=\frac{2\text{x}}{3}-\frac{\text{3x}}{8}=\frac{3\text{x}}{8}$
$=\frac{2\times2}{3}-\frac{3\times2}{8}=\frac{4}{3}-\frac{6}{8}$
$=\frac{4}{3}-\frac{3}{4}=\frac{16-9}{12}=\frac{7}{12}$
$=\frac{7}{12}=\text{R.H.S}$
$\frac{16\text{x}-9\text{x}}{24}=\frac{7}{12}$ (L.C.M of 3, 8 = 24)
$\frac{7\text{x}}{24}=\frac{7}{12}$
Dividing by $\frac{7}{24}$
$=\frac{7\text{x}}{24}+\frac{7}{24}=\frac{7}{12}+\frac{7}{24}$
$\Rightarrow\frac{7\text{x}}{24}\times\frac{24}{7}=\frac{7}{12}\times\frac{24}{12}$
$\Rightarrow\text{x}=2$
$\therefore\text{x}=2$
Verification:
$\text{L.H.S}$ $=\frac{2\text{x}}{3}-\frac{\text{3x}}{8}=\frac{3\text{x}}{8}$
$=\frac{2\times2}{3}-\frac{3\times2}{8}=\frac{4}{3}-\frac{6}{8}$
$=\frac{4}{3}-\frac{3}{4}=\frac{16-9}{12}=\frac{7}{12}$
$=\frac{7}{12}=\text{R.H.S}$
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