Match each equation or inequality in Column I with the graph o...

Question

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

Matching exercise showing absolute value equations and inequalities paired with number line graphs of their solution sets.

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 eight. We're given a number line here to graph that. So starting with what we're given, we have the absolute value of X is greater than eight. And when we have inequalities dealing with the absolute value, we want to think about the two possible cases we get and we call that the absolute value is defined in two parts. So if X is greater than or equal to zero and it's positive, then the absolute value of X is just going to be equal to X by definition. OK. The absolute value of X is always gonna give us a positive value back. So if X is already positive, we just get that X value back. OK. So in that case, our inequality becomes X is greater than, hey, OK. So that's the first half. Now, what about the second half? What happens if X is negative? If X is less than zero, then the absolute value of X is equal to negative X. OK. Again, by definition, recall that definition of the absolute value. If X is negative, we want the absolute value to give us the positive number. So we're gonna multiply by a negative, a negative multiplied by a negative will give us that positive value we're looking for. So if we have the absolute value of X equal to negative X, our inequality becomes negative X is greater than eight. We can divide most sides by negative one to get X by itself. OK. When we do that, remember that you have to switch, switch the sign of the inequality. And if we divide by a negative, we flip the inequality. And so we get that X is less than negative A. OK. So we have these two cases to our solution X can be greater than eight or X could be less than negative eight if we graph these on our number line and we're gonna graph them in red. So it's easy to see for the first one X greater than eight. So we're gonna go to eight and we're gonna draw an open circle. OK. We have strict inequalities here. We do not have X greater than, or equal to eight. So the open circle indicates that we are not including X equals eight. Mm. Now we want X greater than eight. So all of the X values that are greater than eight are to the right. And so we're gonna have a line pointing to the right to include all of those values to the right of that point. And then for X less than negative eight, again, we're gonna go to negative eight, draw an open circle because we're not including exactly that point X equals negative eight. We want X values less than negative eight, which are gonna be to the left. And so we're gonna draw a line to the left to include all of the possible values to the left. And that is the graph of the solution set for this problem that we were looking for. 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

Key Concepts

Absolute Value Inequalities

Graphing Solution Sets on a Number Line

Inequality Notation and Interpretation

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