Question

A rational umber is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12. Find the rational number.
plss plss give correct answer with steps

Answer 1

Let it be p /q .

Now ,

p/q×5/2= -7/12

p/q + 2/3 = -7/12 .

Now,

5p/2q= -7/12

p= -7/12 × 2q/5

= -14/60q

p = -7/30q......1

Also,

p/q +2/3= -7/12

p/q= -7/12-2/3

= -7/12 - 8/12

= -15/12

= -5/4

So , 4p= -5q

Putting p= -5q/4 in eq 1 ,

-5q/4=-7/30q

Image of its solving is attached .

q=0 .

p= -7/30q

=0

Fraction does not exist .Yes , it is the answer.Maybe there ud be some fault in question.

Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get -7/12.

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The rational number.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the rational number be r

A/q

$\longrightarrow\sf{r\times \dfrac{5}{2} +\dfrac{2}{3} =\dfrac{-7}{12} }\\\\\\\longrightarrow\sf{\dfrac{5r}{2} +\dfrac{2}{3} =\dfrac{-7}{12} }\\\\\\\longrightarrow\sf{\dfrac{5r}{2} =\dfrac{-7}{12} -\dfrac{2}{3} }\\\\\\\longrightarrow\sf{\dfrac{5r}{2} =\dfrac{-7-8}{12} }\\\\\\\longrightarrow\sf{\dfrac{5r}{2} =\dfrac{-15}{12} }\\\\\\\longrightarrow\sf{12\times 5r=-15\times 2}\\\\\\\longrightarrow\sf{60r=-30}\\\\\\\longrightarrow\sf{r=\cancel{\dfrac{-30}{60} }}$

$\longrightarrow\sf{\pink{r=-1/2}}$

Thus;

$\star\underbrace{\bf{The\:rational\:number=r=-1/2}}}}}$