Solve each of the following equations and also check your results in each case:

(i) $\frac{2 x + 5}{3} = 3 x - 10$

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Solution

Given: $\frac{2 x + 5}{3} = 3 x - 10$

$\Rightarrow \frac{2 x + 5}{3} - 3 x = - 10$

$\Rightarrow \frac{2 x + 5 - 9 x}{3} = - 10$

$\Rightarrow \frac{- 7 x + 5}{3} = - 10$

$\Rightarrow - 7 x + 5 = - 30$

$\Rightarrow - 7 x = - 35$

$\Rightarrow x = \frac{- 35}{- 7}$

$\Rightarrow x = 5$

To check: $\frac{2 x + 5}{3} = 3 x - 10$ for $x = 5$

L.H.S. = $\frac{2 x + 5}{3}$

$= \frac{2 \times 5 + 5}{3}$

$= \frac{15}{3}$

$= 5$

R.H.S $= (3 x - 10)$

$= (3 \times 5 - 10)$

$= (15 - 10)$

$= 5$

$∴ L . H . S = R . H . S$

Hence, the given equation is verified for $x = 5$ .

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Solve each of the following equations and also check your results in each case: (i) 2x+53=3x−10

Solve each of the following equations and also check your results in each case:

(i) $\frac{2 x + 5}{3} = 3 x - 10$