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

\[\frac{0 . 5(x - 0 . 4)}{0 . 35} - \frac{0 . 6(x - 2 . 71)}{0 . 42} = x + 6 . 1\]
\[\text{ or }\frac{(x - 0 . 4)}{0 . 7} - \frac{(x - 2 . 71)}{0 . 7} = x + 6 . 1\]
\[\text{ or }\frac{x - 0 . 4 - x + 2 . 71}{0 . 7} = x + 6 . 1\]
\[\text{ or }- 0 . 4 + 2 . 71 = 0 . 7x + 4 . 27\]
\[\text{ or }0 . 7x = 2 . 71 - 0 . 4 - 4 . 27\]
\[\text{ or }x = \frac{- 1 . 96}{0 . 7} = - 2 . 8\]
\[\text{ Thus, }x = - 2 . 8\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ Substituting }x = - 2 . 8\text{ in the given equation, we get: }\]
\[\text{ L . H . S . }= \frac{0 . 5( - 2 . 8 - 0 . 4)}{0 . 35} - \frac{0 . 6( - 2 . 8 - 2 . 71)}{0 . 42} = \frac{- 1 . 6}{0 . 35} + \frac{3.306}{0 . 42} = - 4 . 571 + 7 . 871 = 3 . 3\]
\[\text{ R . H . S .} = - 2 . 8 + 6 . 1 = - 3 . 3\]
\[ \therefore \text{ L . H . S . = R . H . S . for } x = - 2 . 8\]