Question
$0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
✓
Answer
$0.5\text{x}+\frac{\text{x}}{3}=0.25\text{x}+7$
$\frac{5}{10}\text{x}+\frac{\text{x}}{3}=\frac{25\text{x}}{100}+7$
$\frac{\text{x}}{2}+\frac{\text{x}}{3}=\frac{\text{x}}{4}+7$
Transposing $\frac{\text{x}}{4}$ to $L.H.S$., we get
$\frac{\text{x}}{2}+\frac{\text{x}}{3}-\frac{\text{x}}{4}=7$
$\frac{65\text{x}+4\text{x}-\text{3x}}{12}=7$
Multiplying both sides by $12$, we get
$\frac{7\text{x}}{12}\times12=7\times12$
$=\text{7x}=84$
Dividing both sides by $7$, we get
$=\frac{7\text{x}}{7}=\frac{84}{7}$
$=\text{x}=12$
Verification:
Substituting $x = 12$ on both sides, we get
$0.5(12) + \frac{12}3 = 0.25(12) + 7$
$6 + 4 = 3 + 7$
$10 = 10$
$L.H.S. = R.H.S.$
Hence, verified.
$\frac{5}{10}\text{x}+\frac{\text{x}}{3}=\frac{25\text{x}}{100}+7$
$\frac{\text{x}}{2}+\frac{\text{x}}{3}=\frac{\text{x}}{4}+7$
Transposing $\frac{\text{x}}{4}$ to $L.H.S$., we get
$\frac{\text{x}}{2}+\frac{\text{x}}{3}-\frac{\text{x}}{4}=7$
$\frac{65\text{x}+4\text{x}-\text{3x}}{12}=7$
Multiplying both sides by $12$, we get
$\frac{7\text{x}}{12}\times12=7\times12$
$=\text{7x}=84$
Dividing both sides by $7$, we get
$=\frac{7\text{x}}{7}=\frac{84}{7}$
$=\text{x}=12$
Verification:
Substituting $x = 12$ on both sides, we get
$0.5(12) + \frac{12}3 = 0.25(12) + 7$
$6 + 4 = 3 + 7$
$10 = 10$
$L.H.S. = R.H.S.$
Hence, verified.
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