Question

The additive inverse of \[\left( { - 9 + 11} \right)\] is:
A. -2
B. 3
C. 9
D. -11

Answer 1

Hint: The additive inverse of a number \[x\] is the number that, when added to \[x\] the sum becomes zero. In other words, the negative of the number \[x\] i.e. \[- x\] is the additive inverse of \[x\].

Complete step-by-step answer:
Consider \[x\] be the additive inverse \[\left( { - 9 + 11} \right)\].
Now, from the definition of the additive inverse, if \[x\] is added with \[\left( { - 9 + 11} \right)\], the sum becomes 0. Therefore,
\[\begin{gathered}
  \,\,\,\,\,\,\left( { - 9 + 11} \right) + x = 0 \\
   \Rightarrow 2 + x = 0 \\
\end{gathered}\]
Now, subtract 2 from both sides of the above expression, to obtain the value of \[x\].
\[\begin{gathered}
  \,\,\,\,\,\,2 + x - 2 = - 2 \\
   \Rightarrow x = - 2 \\
\end{gathered}\]
Thus, the additive inverse of \[\left( { - 9 + 11} \right)\] is -2, hence, option (A) is the correct answer.

Note: The multiplicative inverse of a number \[x\] is the number that, when multiplied with \[x\] the product becomes zero. In other words, the inverse of the number \[x\] i.e. \[{x^{ - 1}}\] is the
multiplicative inverse of\[x\].