Question

The additive inverse of $6$ is ________.
(A) $6$
(B) $ - 6$
(C) $0$
(D) $1$

Answer 1

Hint: Assume the additive inverse of $6$ to be any variable. Then find the sum of $6$ and its inverse and equate it to 0. By adding or subtracting numbers from both sides, find the value of the variable.

Complete step-by-step solution:
Let the additive inverse of $6$ be x.
The additive inverse of a number is the number which when added to the given number yields $0$.
So, find the sum of $6$ and its inverse.
Since we assumed the additive inverse of $6$ to be x.
So, the sum of $6$ and \[x\] will be $6 + x$.
It is equating the sum to $0$.
$6 + x = 0$
Subtract \[6\] from both sides of the equation.
$6 + x - 6 = 0 - 6$
Perform the subtraction among constants.
$x = - 6$
So, the additive inverse of $6$ is $ - 6$.
Thus, (B) is the correct option.

Note: An additive inverse of a number is defined as the value, which on adding with the original number results in zero value. It is the value we add to a number to yield zero. Suppose, a is the original number, then its additive inverse will be minus of a i.e., $ - a$, such that;
$a + \left( { - a} \right) = a - a = 0$.
Example:
Additive inverse of $10$ is $ - 10$, as $10 + \left( { - 10} \right) = 0$.
Additive inverse of $ - 9$ is $9$, as $\left( { - 9} \right) + 9 = 0$.
Additive inverse is also called the opposite of the number, negation of number or changed sign of original number.
Additive inverse of zero is zero.
Properties:
Additive inverse simply means changing the sign of the number and adding it to the original number to get an answer equal to 0.
The properties of additive inverse are given as follows; it is based on negation of the original number.
For example, if we take \[x\] as the original number, then its additive inverse is $ - x$.
So, here we will see the properties of $ - x$.
$ - \left( { - x} \right) = x$
${\left( { - x} \right)^2} = {x^2}$
$ - \left( {x + y} \right) = \left( { - x} \right) + \left( { - y} \right)$
$ - \left( {x - y} \right) = y - x$
$x - \left( { - y} \right) = x + y$
$\left( { - x} \right) \times y = x \times \left( { - y} \right) = - \left( {x \times y} \right)$
$\left( { - x} \right) \times \left( { - y} \right) = x \times y$