Question

Question 13
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 therational numberbex.
According to the question, $\frac{5}{2}x+\frac{2}{3}=-\frac{7}{12}$
$\Rightarrow \frac{5}{2}x+\frac{2}{3}-\frac{2}{3}=\frac{-7}{12}-\frac{2}{3}$ [Subtracting $\frac{2}{3}$ from both sides]
$\Rightarrow \frac{5x}{2}=\frac{-7-8}{12}$
$\Rightarrow \frac{5x}{2}=\frac{-15}{12}$
$\Rightarrow 5x\left(12\right)=-15\times 2$
$\Rightarrow 60x=-30$
$\Rightarrow \frac{60x}{60}=\frac{-30}{60}$ [Dividing both sides by 60]
$\Rightarrow x=\frac{-1}{2}$
Hence,the rational number is
$\frac{-1}{2}$.