# Solve the Following Equation and Also Check Your Result: 6 . 5 X + 19 . 5 X − 32 . 5 2 = 6 . 5 X + 13 + ( 13 X − 26 2 ) - Mathematics

Sum

Solve the following equation and also check your result:
$6 . 5x + \frac{19 . 5x - 32 . 5}{2} = 6 . 5x + 13 + \left( \frac{13x - 26}{2} \right)$

#### Solution

$6 . 5x + \frac{19 . 5x - 32 . 5}{2} = 6 . 5x + 13 + \frac{13x - 26}{2}$
$\text{ or }\frac{19 . 5x - 32 . 5}{2} - \frac{13x - 26}{2} = 13$
$\text{ or }\frac{19 . 5x - 32 . 5 - 13x + 26}{2} = 13$
$\text{ or }6 . 5x - 6 . 5 = 26 [\text{ After cross multiplication }]$
$\text{ or }6 . 5x = 26 + 6 . 5$
$\text{ or }x = \frac{32 . 5}{6 . 5} = 5$
$\text{ Thus, }x = 5\text{ is the solution of the given equation . }$
$\text{ Check: }$
$\text{ Substituting }x = 5\text{ in the given equation, we get: }$
$\text{ L . H . S .} = 6 . 5 \times 5 + \frac{19 . 5 \times 5 - 32 . 5}{2} = 65$
$\text{ R . H . S . }= 6 . 5 \times 5 + 13 + \frac{13 \times 5 - 26}{2} = 65$
$\therefore \text{ L . H . S . = R . H . S . for }x = 5 .$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 9 Linear Equation in One Variable
Exercise 9.2 | Q 23 | Page 12