Question

a rational number is such that when you multiply it by
$\frac{5}{2}$
and add
$\frac{2}{3}$
to the product you get
$- \frac{7}{12}$

What is the number​

Answer 1

let the number be x.

so, (x*5/2) 2/3 = -7/12

5x/2 + 2/3 = -7/12

(15x + 4) /6 = -7/12

[since LCM of 3 and 2 is 6]

12(15x+4) = 6*-7

[ by Cross multiply]

180x + 48 = -42

180x = -42-48

180x = -90

x = -90/180

x = -1/2

so, rational number is -1/2.

hope it will help you

good luck