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

(xx) $\frac{5 (7 x + 5)}{3} - \frac{23}{3} = 13 - \frac{4 x - 2}{3}$

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Solution

Given : $\frac{5 (7 x + 5)}{3} - \frac{23}{3} = 13 - \frac{4 x - 2}{3}$

$\frac{35 x + 25}{3} + \frac{4 x - 2}{3} = 13 + \frac{23}{3}$

$\frac{35 x + 25 + 4 x - 2}{3} = \frac{39 + 23}{3}$

$\frac{39 x + 23}{3} = \frac{62}{3}$

39x + 23 = 62

39x = 62 - 23

39x = 39

x = 1

To chech: $\frac{5 (7 x + 5)}{3} - \frac{23}{3} = 13 - \frac{4 x - 2}{3} f o r x = 1$

$L . H . S . = \frac{5 (7 x + 5)}{3} - \frac{23}{3}$

$= \frac{35 x + 25}{3} - \frac{23}{3}$

$= \frac{35 (1) + 25}{3} - \frac{23}{3}$

$= \frac{60}{3} - \frac{23}{3}$

$= \frac{60 - 23}{3}$

= $\frac{37}{3}$

$R . H . S . = 13 - \frac{4 x - 2}{3}$

$= 13 - \frac{4 (1) - 2}{3}$

$= 13 - \frac{2}{3}$

$= \frac{39 - 2}{3}$

$= \frac{37}{3}$

$∴ L . H . S . = R . H . S .$

Hence, the given equation is verified for x= 1.

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