Question

A rational number's 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 $x$
$\frac{5}{2}x+\frac{2}{3}=\frac{-7}{12}$

Transpose $\frac{2}{3}$ to RHS
$\frac{5x}{2}=\frac{-7}{12}-\frac{2}{3}$

$\Rightarrow \frac{5}{2}x=\frac{-15}{12}$

$\Rightarrow x=-\frac{1}{2}$

Rational number $=-\frac{1}{2}$