A rational number is such that when you multiply it tar and add to the product
you get what is the number.
Answers
Answer
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
) A rational number is such that when you multiply it by \frac{5}{2}
2
5
and add \frac{2}{3}
3
2
to the product, you get -\frac{7}{12}−
12
7
. What is the number?
Solution
Transcript
Solution:
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