question_answer

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?

Answer:

Let the rational number be x

\[\frac{5}{2}x+\frac{2}{3}=\frac{-7}{12}\]

or,        \[\frac{5}{2}x=\frac{-7}{12}-\frac{2}{3}\]

[Transposing \[\frac{2}{3}\]to RHS]

or,        \[\frac{5}{2}x=\frac{-7-8}{12}\]

or,        \[\frac{5}{2}x=\frac{-15}{12}\]

or, \[5x\times 12=-15\times 2\]

or, \[60x=30\] [Dividing both sides by 60]

or, \[x=\frac{-30}{60}\]

or, \[x=\frac{-1}{2}\]

Hence, the required rational number is \[\frac{-1}{2}.\]