Question

Solve each of the following equation and also check your result in each case:
$\frac{0.5(x-0.4)}{0.35}-\frac{0.6(x-2.71)}{0.42}=x+6.1$

Answer 1

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