Question

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

(xxii) $\frac{0.5(x-0.4)}{0.35}-\frac{0.6(x-2.71)}{0.42}=x+6.1$

Answer 1

Given : $\frac{0.5(x-0.4)}{0.35}-\frac{0.6(x-2.71)}{0.42}=x+6.1$

$\left(\frac{0.5}{0.35}\right)(x-0.4)-\left(\frac{0.6}{0.42}\right)(x-2.71)=x+6.1$

$\frac{x-04}{0.7}-\frac{x-2.71}{0.7}=x+6.1$

$\frac{x-0.4-x+2.71}{0.7}=x+6.1$

-0.4 + 2.71 = 0.7 (x + 6.1)

0.7x = 2.71 - 0.4 - 4.27

0.7x = -1.96

$x=-\frac{1.96}{0.7}$

$\therefore x=-2.8$

To check : $\frac{0.5(x-0.4)}{0.35}-\frac{0.6(x-2.71)}{0.42}=x+6.1forx=-2.8$

$L.H.S.=\frac{0.5(x-0.4)}{0.35}-\frac{0.6(x-2.71)}{0.42}$

$=\frac{0.5(-2.8-0.4)}{0.35}-\frac{0.6(-2.8-2.71)}{0.42}$

$=-\frac{1.6}{0.35}+\frac{3.306}{0.42}$

$=\frac{1}{0.07}(-\frac{1.6}{5}+\frac{3.306}{6})$

$=\frac{1}{0.07}(-0.32+0.551)$

$=\frac{1}{0.07}\left(0.231\right)$
= 3.3
R.H.S. = x + 6.1
=-2.8 + 6.1
= 3.3
$\therefore L.H.S.=R.H.S.$

Hence, the given equation is verified for x = -2.8.