Find the solution of the following equations . Also , verify your answer .
$2 (x - 5) + 3 (x + 6) = 12$ .

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Solution

Given , the linear equation is $2 (x - 5) + 3 (x + 6) = 12 - - - - - - - - - - (1)$
$\Rightarrow 2 x - 2 \times 5 + 3 x + 3 \times 6 = 12$
$\Rightarrow 2 x - 10 + 3 x + 18 = 12$
$\Rightarrow 5 x + 8 = 12$
$\Rightarrow 5 x = 12 - 8$
$\Rightarrow 5 x = 4$
$\Rightarrow x = \frac{4}{5}$
So, the required solution of given equation is $x = \frac{4}{5}$ .
Check :- Putting $x = \frac{4}{5}$ in the equation $(1)$ , we get
LHS $= 2 (\frac{4}{5} - 5) + 3 (\frac{4}{5} + 6)$
$= 2 (\frac{4 - 25}{5}) + 3 (\frac{4 + 30}{5})$
$= 2 (\frac{- 21}{5}) + 3 (\frac{34}{5})$
$= (\frac{- 42}{5}) + (\frac{102}{5})$
$= - \frac{42}{5} + \frac{102}{5}$
$= \frac{60}{5}$
$= 12$
Since, LHS $=$ RHS $=$ $12$
Hence, solution $x = \frac{4}{5}$ is satisfy the given equation .

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