Question

Solve the following equation and also check your result:

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

Answer 1

$$\frac{0.5(x-0.4)}{0.35}-\frac{0.6(x-2.71)}{0.42}=x+6.1$$
$$\text{ or }\frac{(x-0.4)}{0.7}-\frac{(x-2.71)}{0.7}=x+6.1$$
$$\text{ or }\frac{x-0.4-x+2.71}{0.7}=x+6.1$$
$$\text{ or }-0.4+2.71=0.7x+4.27$$
$$\text{ or }0.7x=2.71-0.4-4.27$$
$$\text{ or }x=\frac{-1.96}{0.7}=-2.8$$
$$\text{ Thus, }x=-2.8\text{ is the solution of the given equation . }$$
$$\text{ Check: }$$
$$\text{ Substituting }x=-2.8\text{ in the given equation, we get: }$$
$$\text{ L . H . S . }=\frac{0.5(-2.8-0.4)}{0.35}-\frac{0.6(-2.8-2.71)}{0.42}=\frac{-1.6}{0.35}+\frac{3.306}{0.42}=-4.571+7.871=3.3$$
$$\text{ R . H . S .}=-2.8+6.1=-3.3$$
$$\therefore \text{ L . H . S . = R . H . S . for }x=-2.8$$