In Exercises 137–140, determine whether each statement is true or...

Question

In Exercises 137–140, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.

The equation |x| = - 6 is equivalent to x = 6 or x = - 6.

Accepted Answer

Hello. Today we're going to determine whether the given statement is true or false. So the statement says that the absolute value of four X is equal to negative eight and when solving for X is going to produce X is equal to two or X is equal to negative two. Well, in order to figure this out, let's just go ahead and think about what it means to take an absolute value. So let's suppose that we have the absolute value of negative six. Well when you're solving an absolute value or you're trying to get rid of this, the absolute value means that you only take the num numerical value that the number represents. Well, native six on a number line is six units away from zero but that's still a total distance of six. So essentially the absolute value allows you to represent any number as a positive number. So in this case here negative six can be represented as six through the absolute value. What that means is any time you have a number inside an absolute value. It spits out a number that is always going to be greater than or equal to zero. Now the statement given to us is saying that the absolute value of four X is going to equal to a negative number and that's not going to be true because no matter what value of X you plug in for this statement, it's always going to produce a number that is greater than or equal to zero. So with that being said, the answer to this problem is going to be d The absolute value cannot be less than zero. So I hope this video helps you in understanding whether they determined this is true or false, and I'll go ahead and see you all in the next video.

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