Q.13 A rational number is such that when you multiply it by  $\frac{5}{2}$  and add  $\frac{2}{3}$  to the product, you get  $\frac{-7}{12}$ . What is the number?

Let the rational number be x.

According to the question,

$x\times \frac{5}{2} + \frac{2}{3} = -\frac{7}{12}$

Transposing $\frac{2}{3}$  to the RHS:

$x\times \frac{5}{2} = -\frac{7}{12} - \frac{2}{3} = \frac{-15}{12} = \frac{-5}{4}$

Multiplication by 2 in both sides, we get

$5x = \frac{-5}{4}\times 2 = \frac{-5}{2}$

Dividing both sides by 5, we get

$x = \frac{-5}{2}\times \frac{1}{5} = \frac{-1}{2}$

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