Match each equation or inequality in Column I with the graph of
its solution set in Column II. | x | ≥ 7

Question

Accepted Answer

Hey, everyone in this problem, we're asked to graph the solution set for the following inequality. We know that the absolute value of X is greater than or equal to nine. And we're given a number line here to draw out our solution. So starting with what we're given, we have the absolute value of X is greater than or equal to nine. We have an absolute value inequality. One thing we can do is think about two different cases that we have. OK. So the first case is if X is the positive value, OK. So if X is greater than or equal to zero, what happens? Well, the absolute value of X is just going to be equal to X. OK? Remember that the absolute value always gives us a positive number out of it. OK? So if X is already positive, the absolute value just gives us that X value back. The absolute value of X is just equal to X, then our inequality becomes X is greater than or equal to nine. So we have X has to be greater than or equal to zero, X is greater than or equal to nine. In case two what happens if X is negative, if X is less than zero, then the absolute value of X is going to be equal to negative X. OK? And this is by definition of that absolute value, if we have a negative value inside of our absolute value, OK. We're gonna multiply it by a negative to get a positive result. So writing our inequality in this case, we have that negative X is greater than or equal to nine. We can divide by negative one. Remember that when we divide by a negative or inequality has to flip. And so we get that X is less than or equal to negative oops negative nine. Sorry X is less than or equal to negative nine. OK. So we have two solutions X is greater than or equal to nine and X is less than or equal to negative nine. If we draw these out on our graph or on a number line, OK. For negative nine, we draw a circle, we're including that end point and we want all the X values less than negative nine. So we're gonna include a line going to the left of negative nine, including all of those values. And then for X greater than or equal to nine. Again, we draw a close circle at X equals nine to indicate that we include that end point, we want all the X values bigger then so we're drawing a line to the right to include all those X values greater then and that's gonna be the graph of our solution set for this problem. Thanks everyone for watching. I hope this video helped see you in the next one.

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | ≥ 7

Verified Solution

Key Concepts

Inequalities

Graphing Solutions

Interval Notation