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

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, we have that the absolute value of X is less than three. And we're given a number line to draw this in. So starting with the absolute value of X is less than three, OK? We wanna notice that three is positive. OK? It's greater than zero. And so recall that if three is positive and we have the absolute value of X a less than some positive value, we can rewrite this as negative three is less than X which is less than three. OK? And that comes from the fact that we can split that in a or the absolute value sorry into two cases if X is positive and if X is negative, OK. So if you forget this little trick to get to this in a quality, you can always split your absolute value into two cases. The positive case, the negative case and you're gonna get the same result. OK? So now that we have this inequality for our solution, we wanna go ahead and grab it. So we want the interval between negative three and three and we are not including those end points. OK? We did not have less than are equal to in our original um inequality. And so we do not have less than are equal to in our um solution inequality. So we're gonna have open circles at negative three and at positive three to indicate that we are not including those X values. And then we're gonna include all of the points in between. So we're gonna draw a line connecting those two points to indicate that we're including all X values in between those two points. And that's it. That's the graph of the solution set for this problem. Like we were asked to find, 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