Question

Verify $ - ( - x) = x$ for $x = \dfrac{2}{{15}}$.

Answer 1

Hint: We are given a number which is a fraction and asked to verify that taking two times negative of the number will result in that number itself. For that, we have to multiply the given number by $ - 1$ one after another and see that the same number comes in the end. Thus we can verify the result.

Complete step-by-step answer:
Given $x = \dfrac{2}{{15}}$
We have to verify $ - ( - x) = x$
For, consider $x = \dfrac{2}{{15}}$
Multiplying both sides by $ - 1$ we have,
$ - 1 \times x = - 1 \times \dfrac{2}{{15}}$
Simplifying we get,
$ - x = - \dfrac{2}{{15}}$
Again multiplying both sides by $ - 1$ we have,
$ - 1 \times - x = - 1 \times - \dfrac{2}{{15}}$
$ \Rightarrow - ( - x) = - 1 \times - \dfrac{2}{{15}}$
We know a negative number multiplied by another negative number will result in a positive number.
Also $1 \times \dfrac{2}{{15}} = \dfrac{2}{{15}}$
So we have,
$ - ( - x) = \dfrac{2}{{15}}$
But it is given $x = \dfrac{2}{{15}}$
So we get,
$\therefore - ( - x) = x$ for $x = \dfrac{2}{{15}}$
Hence the result is verified.

Note: For a number $x$, the number $ - x$ is called the additive inverse of $x$, since $x + ( - x) = 0$.
Similarly there are multiplicative inverses too.
For a number $x$, the number $\dfrac{1}{x}$ is called the multiplicative inverse of $x$. A number multiplied by its multiplicative inverse is one.