question_answer

Verify that \[-\text{ }\left( -\text{ }x \right)\text{ }=\text{ }x\]for

(a) \[x=\frac{11}{15}\]

(b) \[x=-\frac{13}{17}\]

Answer:

(a) we have \[x=\frac{11}{15}\]

The additive inverse of \[x=\frac{11}{15}\]is \[\text{ }x=\frac{11}{15}\],

Since \[\frac{11}{15}+\left( \frac{-11}{15} \right)=0.\]

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

i.e.,\[\text{ }\left( \text{ }x \right)\text{ }=\text{ }x\]                     Hence Verified

(b) The additive inverse of x = \[\frac{-13}{17}\]is \[-x=\frac{13}{17},\] since \[\frac{-13}{17}+\frac{13}{17}=0.\]

The same equality \[\frac{-13}{17}+\frac{13}{17}=0.\] shows that the additive inverse of\[\frac{13}{17}\]is \[-\frac{13}{17}\] i.e., \[\left( \text{ }x \right)=x\]

Hence Verified