Question
Solve the following equations by trial and error method:
$\frac{\text{x}}{2}+7=11$
$\frac{\text{x}}{2}+7=11$
✓
Answer
$\frac{\text{x}}{2}+7=11$
Here, $\text{L.H.S.} = \frac{\text{x}}{2}+7$ and $R.H.S. = 11$.
Since $R.H.S.$ is a natural number, $\frac{\text{x}}{2}$ must also be a natural number, so we must substitute values of $x$ that are multiples of $2$.
Therefore, if $x = 8, L.H.S. = R.H.S$.
Hence, $x = 8$ is the solution to this equation.
Here, $\text{L.H.S.} = \frac{\text{x}}{2}+7$ and $R.H.S. = 11$.
Since $R.H.S.$ is a natural number, $\frac{\text{x}}{2}$ must also be a natural number, so we must substitute values of $x$ that are multiples of $2$.
| x | L.H.S. | R.H.S. | Is L.H.S. = R.H.S. |
| $2$ | $\frac{2}{2}+7=8$ | $11$ | No |
| $4$ | $\frac{4}{2}+7=9$ | $11$ | No |
| $6$ | $\frac{6}{2}+7=10$ | $11$ | No |
| $8$ | $\frac{8}{2}+7=11$ | $11$ | Yes |
Hence, $x = 8$ is the solution to this equation.
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