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

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 following inequality. And we want the absolute value of X to be greater than negative four. So let's think about this in a couple of different ways. OK? We have the absolute value of X greater than negative four. The first thing we wanna see notice is that you know what the absolute value always gives us a positive number. OK? If it always gives us a positive number, then it's always gonna be greater than negative four. OK? So we know that the absolute value of X is always greater than or equal to zero, which tells us that all values of X are true. OK? So we can have X from negative infinity all the way up to positive infinity. Any X value satisfies this inequality. Now, if you didn't notice that right off the bat and you wanted to go ahead and solve this algebraically, let's just show how that would be done. OK? So we have an absolute value. We're gonna break it up into two cases. The first case would be if X is greater than or equal to zero. If X is greater than or equal to zero. Then the absolute value of X is just equal to X. And recall that, that absolute value gives us a positive answer. So if X is already positive, well, then we just get that positive value back. OK. That's by definition of the absolute value. And so our inequality becomes X is greater than negative four. Now for the second case, what if X is negative? If X is negative, then the absolute value of X is equal to negative X by definition, OK, X is negative, we wanna get a positive value out of it. So we multiply it by negative, negative, multiplied by negative gives us a positive. In this case, our inequality becomes negative X is greater than negative four. We're gonna multiply by negative one need to simplify when we do that. We have to remember to flip our inequality because we're dividing by a negative or multiplying by a negative. And we get that X is less than four. OK. So on the left hand side, we have X has to be greater than or equal to zero. And then we end up with X is greater than negative four. OK. So this inequality on the left hand side that we get is actually X is greater than or equal to zero. On the right hand side, this case, we have to have X less than zero. We get that X can be less than four. So we have to take the X is less than zero, that more restrictive case. Ok? But putting the two together X can be greater than, or equal to zero or X can be less than zero. That's just the entire number one. And that's all real values which matches what we said at the beginning. Ok? And that's it, that's our solution set for this problem. It is gonna be that entire number line, any X value. 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

Number Line

Graphing Solutions