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

Question

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

Accepted Answer

Hey, everyone in this problem, we're asked to graph the solution set for the equation. The absolute value of X is not equal to a, OK. We're given a number line here to graph our solution. So let's start with the equation we're given and try to figure out what this is telling us. OK. So the absolute value of X is not equal to a. Now recall that the absolute value of X, we can write this as positive X if X is greater than or equal to zero and we can write it as negative X if X is less than zero. OK. So if we have an absolute value, we have to consider the two cases. OK? So if X is positive, we get the case where we just take X, OK? And we want that not equal to eight. But if X is negative, then we're gonna multiply it. OK by a negative inside of this absolute value and we get negative X is not equal to eight, which tells us that X cannot be equal to negative eight. OK? So we have these two restrictions in our solution. Any other value is OK? And we cannot have the absolute value equal to eight. So we have these two conditions that we have any other value is fine. So if we graph this on our number line, we're gonna do it in red, we're gonna draw circles, open circles at negative eight and positive eight. And the open circles are gonna indicate that we are excluding those points. OK? So we're excluding X equals eight, we're excluding X equals negative eight. and everything else in the number line is gonna be included. So we're gonna draw a line everywhere else. Any other value is OK? And that is gonna be the 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

Key Concepts

Inequalities

Absolute Value

Graphing Solution Sets

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