Which of the following is equal to the opposite of −45? −(−45) −45 −|−45| −|45|

-(-45) and -|45|

Step-by-step explanation:

Opposite of a number can also me termed the conjugate of such number. For example, the conjugate (opposite) of a is -a.

Also any value in the modulus sign can either be a negative or positive value. For example |a| can be +a or -a.

According to the question, we are to find the numbers that are equivalent to opposite of -45 i.e which of them are conjugate of -45.

To do this, we are to select the values in the options that will return +45.

Let's look at each option.

For -(-45):

Since the product of two negative sign will give a positive(+), then -(-45) = +45 and hence the value is opposite of -45

For -45:

-45 is a negative value and can never be positive since 45 is not inside a modulus sign. Hence, -45 is not equal to opposite of -45.

For −|−45|, |-45| can only return a positive value since -45 is already in a modulus sign. What the modulus sign will do is convert it to positive value i.e |-45| = 45. Hence -|-45| ≈ -(45) which is not also equivalent to the opposite of-45.

For -|45|:

The value inside modules will return both +45 and -45, hence it can be written as -|45| = -(-45) = +45. This shows that -|45| is also equivalent to the opposite of -45.

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