Determine whether each statement is true or false. |5+(-13) | = |...

Question

Determine whether each statement is true or false. |5+(-13) | = |5| + |-13|

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to determine if the statement that the absolute value of nine plus negative 21 is equal to the absolute value of nine plus the absolute value of negative 21. And we want to write if that statement is true or false. So in this case because we're working with absolute values, let's recall the absolute value rule which states that if we have the absolute value of a number such as a we get back that number A But if we have the absolute value of a number that is negative such as negative A. We also get back a because the absolute value eliminates any negative sign so we can use that to help us simplify our expression and see if the statement is correct. So we have the absolute value of nine plus negative Is equal to the absolute value of nine plus the absolute value of negative 21. So if I simplify the left hand side I have 9 - or negative 12. And notice I just simplified the inside of the absolute quality. So I still have those absolute value bars and once I get rid of those bars this negative 12 becomes positive 12. So now I can go ahead and start to simplify my right hand side. So the absolute value of nine is nine and the absolute value of negative 21 is positive 21. So my right hand side is 9-plus 21 or 30. And from this you can see that my left hand side and my right hand side are not equal, which means that this statement is false. So you can see that aligns with answer choice B. Hopefully this video helped and see you next time.

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Determine whether each statement is true or false. |5+(-13) | = |5| + |-13|