Question

Which statement is true? Question 1 options: A) – |–13| = 13 B) – |13| = 13 C) |–13| = 13 D) |13| = – 13

Answer 1

Answer:

The answer is C. |-13| = 13

Step-by-step explanation:

The definition of absolute value is:

$\displaystyle \large{ |x| = \begin{cases} x \: \: (x \geqslant 0) \\ - x \: \: (x < 0) \end{cases}}$

To say it simply, any real numbers in absolute sign, when evaluated, they will always be positive.

No matter the positive real numbers or negative real numbers - if these numbers are in absolute sign, they will be evaluated to positive.

Examples

$\displaystyle \large{ |2| = 2} \\ \displaystyle \large{ | - 2| = 2} \\ \displaystyle \large{ | - 8| = 8}$

But if the negative is not inside the absolute sign.

Examples II

$\displaystyle \large{ - |2| = - 2} \\ \displaystyle \large{ - | - 2| = - 2} \\ \displaystyle \large{ - | - 8| = - 8}$

First, we evalute the absolute value first. We know thay any real numbers in absolute sign will become positive. Next, after evaluating the absolute value, we simply add the negative symbol beside the positive number.

Simplified Definition

This one is to make it simple to remember.

$\displaystyle \large{ |a| = a} \\ \displaystyle \large{ | - a| = a} \\ \displaystyle \large{ - |a| = - a} \\ \displaystyle \large{ - | - a| = - a}$

After reading the explanation, see the choices and tell if they are true or not.

The A choice is wrong as we know that -|-13| is -13.

The B choice is wrong, the reason is same as the A choice.

The C choice is correct! Any real numbers in absolute sign are always positive.

The D choice is wrong because absolute-value numbers cannot be negative, refer to the C choice's reason.

Let me know if you have any questions!