Question

Solve the following equation and also check your result:
\[x - 2x + 2 - \frac{16}{3}x + 5 = 3 - \frac{7}{2}x\]

Answer 1

\[x - 2x + 2 - \frac{16}{3}x + 5 = 3 - \frac{7}{2}x\]
\[\text{ or }\frac{3x - 6x + 6 - 16x + 15}{3} = \frac{6 - 7x}{2}\]
\[\text{ or }\frac{- 19x + 21}{3} = \frac{6 - 7x}{2}\]
\[\text{ or }- 38x + 42 = 18 - 21x\]
\[\text{ or }- 21x + 38x = 42 - 18\]
\[\text{ or }17x = 24\]
\[\text{ or }x = \frac{24}{17}\]
\[\text{ Check: }\]
\[\text{ L . H . S .} = \frac{24}{17} - 2 \times \frac{24}{17} + 7 - \frac{16}{3} \times \frac{24}{17} = \frac{- 33}{17}\]
\[\text{ R . H . S . }= 3 - \frac{7}{2} \times \frac{24}{17} = \frac{- 33}{17}\]
∴  L.H.S. = R.H.S. for x = \[\frac{24}{17}\]