Solve each of the following equations and also verify your solution :

$\frac{5 x}{3} + \frac{2}{5} = 1$

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Solution

$\frac{5 x}{3} + \frac{2}{5} = 1$
Substractig $\frac{2}{5}$ from both sides:
$\frac{5 x}{3} + \frac{2}{5} - \frac{2}{5} = 1 - \frac{2}{5} \Rightarrow \frac{5 x}{3} = \frac{3}{5}$
$\Rightarrow$ Multiplying $\frac{3}{5}$ both sides
$\frac{5}{3} x \times \frac{3}{5} = \frac{3}{5} \times \frac{3}{5} \Rightarrow x = \frac{9}{25}$
Verification:
$L . H . S . = \frac{5 x}{3} + \frac{2}{5} = \frac{5}{3} \times \frac{9}{25} + \frac{2}{5} = \frac{3}{5} + \frac{2}{5} = \frac{3 + 2}{5} = \frac{5}{5} = 1 = R . H . S .$

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