Solve each of the following equation and also check your result in each case:

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

or $\frac{(\mathrm{x}-0.4)}{0.7}-\frac{(\mathrm{x}-2.71)}{0.7}=\mathrm{x}+6.1$

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

or $-0.4+2.71=0.7 x+4.27$

or $0.7 \mathrm{x}=2.71-0.4-4.27$

or $\mathrm{x}=\frac{-1.96}{07}=-2.8$

Thus, $x=-2.8$ is the solution of the given equation.

Check:

Substituting $\mathrm{x}=-2.8$ in the given equation, we get:

L. H.S. $=\frac{0.5(-2.8-0.4)}{0.35}-\frac{0.6(-2.8-2.71)}{0.42}=\frac{-1.6}{0.35}+\frac{3.306}{0.42}=-4.571+7.871=3.3$

R. H.S. $=-2.8+6.1=-3.3$

$\therefore$ L. H.S. $=$ R. H. S. for $\mathrm{x}=-2.8$