Question

Verify that: $-(-x)=x$ for $x=\frac{11}{15}$.

Answer 1

Verifying $-(-x)=x$ for given $x$:

Additive Inverse: An additive inverse of a number is another number, which on adding with the original number gives $0$. It is the value we add to a number to yield zero.

Suppose, $a$ is the original number, then its additive inverse will be $(-a)$, such that;

$a+(-a)=a–a=0$

Therefore,the additive inverse of $x$ is $-x$.

Since, $x+(-x)=x-x=0$

Therefore, the additive inverse of $\frac{11}{15}$ is $\frac{-11}{15}$

Since, $\frac{11}{15}+\left(\frac{-11}{15}\right)=\frac{11}{15}-\frac{11}{15}=0$

Hence, the same equality $\frac{11}{15}+\left(\frac{-11}{15}\right)=\frac{11}{15}-\frac{11}{15}=0$ , shows that the additive inverse of $\frac{-11}{15}$ is $\frac{11}{15}$.

Or we can write like that, $-\left(\frac{-11}{15}\right)=\frac{11}{15}$

i.e., $-(-x)=x$

Hence, verified.