Question
Solve the following equation and also check your result in case: $6.5\text{x}+\frac{19.5\text{x}-32.5}{2}=6.5\text{x}+13+\Big(\frac{13\text{x}-26}{2}\Big)$
✓
Answer
$6.5\text{x}+\frac{19.5\text{x}-32.5}{2}=6.5\text{x}+13+\frac{13\text{x}-26}{2}$
$\frac{19.5\text{x}-32.5}{2}-\frac{13\text{x}-26}{2}=13$
$\frac{19.5\text{x}-32.5-13\text{x}+26}{2}=13$
$6.5\text{x}-6.5=26$ [After cross miltiplication]
$6.5\text{x}=26+6.5$
$\text{x}=\frac{32.5}{6.5}=5$
Thus, $\text{x}=5$ is the solution of the given equation.
Check:Substituting $\text{x}=5$ in the given equation,
we get:
$\text{L.H.S.}=6.5\times5+\frac{19.5\times5-32.5}{2}=65$
$\text{R.H.S.}=6.5\times5+13+\frac{13\times5-26}{2}=65$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for x}=5$
$\frac{19.5\text{x}-32.5}{2}-\frac{13\text{x}-26}{2}=13$
$\frac{19.5\text{x}-32.5-13\text{x}+26}{2}=13$
$6.5\text{x}-6.5=26$ [After cross miltiplication]
$6.5\text{x}=26+6.5$
$\text{x}=\frac{32.5}{6.5}=5$
Thus, $\text{x}=5$ is the solution of the given equation.
Check:Substituting $\text{x}=5$ in the given equation,
we get:
$\text{L.H.S.}=6.5\times5+\frac{19.5\times5-32.5}{2}=65$
$\text{R.H.S.}=6.5\times5+13+\frac{13\times5-26}{2}=65$
$\therefore\text{L.H.S.}=\text{R.H.S.}\text{ for x}=5$
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