In Exercises 51–60, rewrite each expression without absolute valu...

Question

In Exercises 51–60, rewrite each expression without absolute value bars. ||-3|-|-7||

Accepted Answer

Hello today we're going to be evaluating an absolute value expression. So the expression given to us is the absolute value of the absolute value of negative eight minus the absolute value of negative 14. So this way we don't get confused by the absolute value symbols. I'm gonna write the outermost absolute value symbols in red and the inside argument is going to be in black. So we're taking the absolute value of the absolute value of negative eight minus the absolute five negative 14. Now how do we start this? Well in order to start evaluating this we're gonna need to evaluate the inside argument of the innermost absolute values. Well how do we evaluate the absolute value of negative eight and the absolute value of negative 14? While the absolute value just represents the absolute distance between two points. And it essentially just allows you to rewrite any numbers inside the absolute value as a positive number. So we can rewrite negative eight as positive eight and negative 14 as positive 14. And what that gives us is the absolute value of positive eight minus 14. And now we just have to evaluate the inside furthermore well -14 Is gonna give us -6. So what we are left with is the absolute value of -6. And once again the absolute value just allows you to represent this as a positive number. So the absolute value of negative six is equal to six which is going to be our solution. And the answer to this problem is going to be a So I hope this video helps you in understanding how to evaluate an absolute value expression, and I'll go ahead and see you all in the next video.