A Rational number is such that when you multiply it by 52 and add 23 to the product ,you get 712. what is the number??
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Step-by-step explanation:
Let the rational number be x.
According to the question, \frac{5}{2}x+\frac{2}{3}=-\frac{7}{12}
2
5
x+
3
2
=−
12
7
\Rightarrow\ \frac{5}{2}x+\frac{2}{3}-\frac{2}{3}=-\frac{7}{12}-\frac{2}{3}⇒
2
5
x+
3
2
−
3
2
=−
12
7
−
3
2
[Subtracting \frac{2}{3}
3
2
from both sides]
\Rightarrow\ \frac{5x}{2}=\frac{-7-8}{12}⇒
2
5x
=
12
−7−8
\Rightarrow\ \frac{5x}{2}=\frac{-15}{12}⇒
2
5x
=
12
−15
\Rightarrow\ 5x\times12=-15\times2⇒ 5x×12=−15×2
\Rightarrow60x=-30⇒60x=−30
\Rightarrow\ \frac{60x}{60}=\frac{-30}{60}⇒
60
60x
=
60
−30
[Dividing both sides by 60]
\Rightarrow\ x=\ \frac{-1}{2}⇒ x=
2
−1
Hence, the rational number is \frac{-1}{2}
2
−1
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