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 \[\frac{-1}{2}.\]
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