# Solve the Following Equation and Also Check Your Result : 4 X 9 + 1 3 + 13 108 X = 8 X + 19 18 - Mathematics

Sum

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

#### Solution

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

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 9 Linear Equation in One Variable
Exercise 9.2 | Q 18 | Page 11