Question

Solve the following equation and also check your result:
\[\frac{4x}{9} + \frac{1}{3} + \frac{13}{108}x = \frac{8x + 19}{18}\]

Answer 1

\[\frac{4x}{9} + \frac{1}{3} + \frac{13}{108}x = \frac{8x + 19}{18}\]
\[\text{ or }\frac{48x + 36 + 13x}{108} = \frac{8x + 19}{18}\]
\[\text{ or }\frac{61x + 36}{108} = \frac{8x + 19}{18}\]
\[\text{ or }61x + 36 = 6(8x + 19) [\text{ Multiplying both sides by }108]\]
\[\text{ or }61x + 36 = 48x + 114\]
\[\text{ or }61x - 48x = 114 - 36\]
\[\text{ or }13x = 78\]
\[\text{ or }x = \frac{78}{13}\]
\[\text{ or }x = 6\]
\[\text{ Thus, }x = 6\text{ is the solution of the given equation . }\]
\[\text{ Check: }\]
\[\text{ Substituting }x = 6\text{ in the given equation, we get: }\]
\[\text{ L . H . S .} = \frac{4 \times 6}{9} + \frac{1}{3} + \frac{13}{108} \times 6 = \frac{24}{9} + \frac{1}{3} + \frac{13}{18} = \frac{48 + 6 + 13}{18} = \frac{67}{18}\]
\[\text{ R . H . S . }= \frac{8 \times 6 + 19}{18} = \frac{67}{18}\]
\[ \therefore \text{ L . H . S . = R . H . S . for }x = 6 .\]