Question

Solve each of the following equation and also check your result in each case:
$6.5x+\frac{19.5x-32.5}{2}=6.5x+13+\left(\frac{13x-26}{2}\right)$

Answer 1

$$\begin{gathered} 6.5\mathrm{x}+\frac{19.5\mathrm{x}-32.5}{2}=6.5\mathrm{x}+13+\frac{13\mathrm{x}-26}{2} \\ \mathrm{or}\frac{19.5\mathrm{x}-32.5}{2}-\frac{13\mathrm{x}-26}{2}=13 \\ \mathrm{or}\frac{19.5\mathrm{x}-32.5-13\mathrm{x}+26}{2}=13 \\ \mathrm{or}6.5\mathrm{x}-6.5=26[\text{After}c\mathrm{ross}\mathrm{multipl}\text{ication}] \\ \mathrm{or}6.5\mathrm{x}=26+6.5 \\ \mathrm{or}\mathrm{x}=\frac{32.5}{6.5}=5 \\ \mathrm{Thus},\mathrm{x}=5\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=5\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=6.5\times 5+\frac{19.5\times 5-32.5}{2}=65 \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=6.5\times 5+13+\frac{13\times 5-26}{2}=65 \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=5. \end{gathered}$$