Question

Solve each of the following equation and also check your result in each case:
$5\left(\frac{7x+5}{3}\right)-\frac{23}{3}=13-\frac{4x-2}{3}$

Answer 1

$$\begin{gathered} 5\left(\frac{7\mathrm{x}+5}{3}\right)-\frac{23}{3}=13-\frac{4\mathrm{x}-2}{3} \\ \mathrm{or}\frac{35\mathrm{x}+25}{3}+\frac{4\mathrm{x}-2}{3}=13+\frac{23}{3} \\ \mathrm{or}\frac{35\mathrm{x}+25+4\mathrm{x}-2}{3}=\frac{39+23}{3} \\ \mathrm{or}39\mathrm{x}+23=62[\mathrm{Multiply}\text{ing}\mathrm{both}\mathrm{sides}\mathrm{by}3] \\ \mathrm{or}39\mathrm{x}=62-23 \\ \mathrm{or}\mathrm{x}=\frac{39}{39} \\ \mathrm{or}\mathrm{x}=1 \\ \mathrm{Thus},\mathrm{x}=1\mathrm{is}\mathrm{the}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{given}\mathrm{equation}. \\ \mathrm{Check}: \\ \mathrm{Substituting}\mathrm{x}=1\mathrm{in}\mathrm{the}\mathrm{given}\mathrm{equation},\mathrm{we}\mathrm{get}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=5\left(\frac{7\times 1+5}{3}\right)-\frac{23}{3}=\frac{60}{3}-\frac{23}{3}=\frac{37}{3} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=13-\frac{4\times 1-2}{3}=\frac{39-2}{3}=\frac{37}{3} \\ \therefore \mathrm{L}.\mathrm{H}.\mathrm{S}.=\mathrm{R}.\mathrm{H}.\mathrm{S}.\mathrm{for}\mathrm{x}=1. \end{gathered}$$