Question

Solve each of the following equation and also check your result in each case:
$x-2x+2-\frac{16}{3}x+5=3-\frac{7}{2}x$

Answer 1

$$\begin{gathered} \mathrm{x}-2\mathrm{x}+2-\frac{16}{3}\mathrm{x}+5=3-\frac{7}{2}\mathrm{x} \\ \mathrm{or}\frac{3\mathrm{x}-6\mathrm{x}+6-16\mathrm{x}+15}{3}=\frac{6-7\mathrm{x}}{2} \\ \mathrm{or}\frac{-19\mathrm{x}+21}{3}=\frac{6-7\mathrm{x}}{2} \\ \mathrm{or}-38\mathrm{x}+42=18-21\mathrm{x} \\ \mathrm{or}-21\mathrm{x}+38\mathrm{x}=42-18 \\ \mathrm{or}17\mathrm{x}=24 \\ \mathrm{or}\mathrm{x}=\frac{24}{17} \\ \mathrm{Check}: \\ \mathrm{L}.\mathrm{H}.\mathrm{S}.=\frac{24}{17}-2\times \frac{24}{17}+7-\frac{16}{3}\times \frac{24}{17}=\frac{-33}{17} \\ \mathrm{R}.\mathrm{H}.\mathrm{S}.=3-\frac{7}{2}\times \frac{24}{17}=\frac{-33}{17} \end{gathered}$$

$\therefore$ L.H.S. = R.H.S. for x = $\frac{24}{17}$