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A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12 . What is the number?

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?

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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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