Question

Solve and check your answer.

\frac{x + 3}{7} - \frac{2 x - 5}{3} = \frac{3 x - 5}{5} - 25

Accepted Answer

Given,

$\frac{x + 3}{7} - \frac{2 x - 5}{3} = \frac{3 x - 5}{5} - 25$

We know that, the process of finding the number a variable represents in an equation is called solving the equation.

So,

$\frac{x + 3}{7} - \frac{2 x - 5}{3} = \frac{3 x - 5}{5} - 25$

$\Rightarrow \frac{3 \times (x + 3)}{3 \times 7} - \frac{7 \times (2 x - 5)}{3 \times 7} = \frac{3 x - 5}{5} - \frac{5 \times 25}{5}$

$\Rightarrow \frac{3 x + 9}{21} - \frac{14 x - 35}{21} = \frac{3 x - 5}{5} - \frac{125}{5}$

$\Rightarrow \frac{3 x + 9 - 14 x + 35}{21} = \frac{3 x - 5 - 125}{5}$

$\Rightarrow \frac{- 11 x + 44}{21} = \frac{3 x - 130}{5}$

$\Rightarrow 5 (- 11 x + 44) = 21 (3 x - 130)$

$\Rightarrow - 55 x + 220 = 63 x - 2730$

$\Rightarrow 63 x + 55 x = 220 + 2730$

$\Rightarrow 118 x = 2950$

$\Rightarrow x = \frac{2950}{118}$

$\Rightarrow x = 25$

So by putting the value of $x$ in given equation we get,

$\frac{x + 3}{7} - \frac{2 x - 5}{3} = \frac{3 x - 5}{5} - 25 \Rightarrow \frac{25 + 3}{7} - \frac{2 \times 25 - 5}{3} = \frac{3 \times 25 - 5}{5} - 25 \Rightarrow - 11 = - 11$

Hence, $x = 25$ is correct answer.

O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Chapter: Linear Equations in One Variable, Exercise 2: Exercise

O P Malhotra Mathematics Solutions for Exercise - O P Malhotra, S K Gupta and, Anubhuti Gangal Solutions for Chapter: Linear Equations in One Variable, Exercise 2: Exercise

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