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?

Let the rational number be x.
According to the question, 5/2x+2/3=-7/12
⇒ 5/2 x+2/3-2/3=-7/12-2/3 [Subtracting 2/3 from both sides]
⇒ 5x/2=-7-8/12 ⇒ 5x/2=-15/12
⇒ 5xX12=-15×2 ⇒ 60x=-30
⇒ 60x/60=-30/60 [Dividing both sides by 60]
⇒ x=-1/2
Hence, the rational number is -1/2

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