Question

Solve each of the following equations and also check your results in each case:

(xxiii) $6.5x+\frac{19.5x-32.5}{2}=6.5x+13+\frac{13x-26}{2}$

Answer 1

Given : $6.5x+\frac{19.5x-32.5}{2}=6.5x+13+\frac{13x-26}{2}$

$6.5x+\frac{19.5x-32.5}{2}-6.5x-\frac{13x-26}{2}=13$

$\frac{19.5x-32.5}{2}-\frac{13x-26}{2}=13$

$\frac{19.5x-32.5-13x+26}{2}=13$

$\frac{6.5x-6.5}{2}=13$

$6.5x-6.5=13\times 2$
6.5x - 6.5 = 26
6.5x = 26 +6.5
6.5x = 32.5
$x=\frac{32.5}{6.5}$
$\therefore x=5$

To check: $6.5x+\frac{19.5x-32.5}{2}=6.5x+13+\frac{13x-26}{2}$
for x= 5
$L.H.S.=6.5x+\frac{19.5x-32.5}{2}$

$=6.5\left(5\right)+\frac{19.5\left(5\right)-32.5}{2}$

$=32.5+\frac{97.5-32.5}{2}$

$=32.5+\frac{65}{2}$

=32.5 + 32.5
= 65

$R.H.S.=6.5x+13+\frac{13x-26}{2}$

$=6.5\left(5\right)+13+\frac{13\left(5\right)-26}{2}$

$=32.5+13+\frac{65-26}{2}$

$=45.5+\frac{39}{2}$

=45.5 + 19.5

=65

$\therefore L.H.S.=R.H.S.$

Hence, the given equation is verified for x=5.