WEBVTT
00:00:01.840 --> 00:00:09.080
Use the graph to find the solution set of the inequality ๐ of ๐ฅ is greater than or equal to ๐ of ๐ฅ.
00:00:10.960 --> 00:00:13.720
Weโll begin by defining our individual functions.
00:00:14.520 --> 00:00:20.440
We can see from the graph that ๐ of ๐ฅ is the absolute value of ๐ฅ plus one.
00:00:21.320 --> 00:00:23.600
๐ of ๐ฅ is given by this horizontal line.
00:00:24.040 --> 00:00:25.880
๐ of ๐ฅ is equal to three.
00:00:26.560 --> 00:00:36.640
So weโre going to use the graph to find the solution set of the inequality the absolute value of ๐ฅ plus one is greater than or equal to three.
00:00:37.600 --> 00:00:45.480
And so, really, to solve this, weโre going to find the values of ๐ฅ such that the graph of ๐ of ๐ฅ is greater than the graph of ๐ of ๐ฅ.
00:00:46.760 --> 00:00:50.760
Well, we can see that thatโs in these two places.
00:00:51.680 --> 00:01:03.680
In fact, since weโre working with a weak inequality โ that is, the absolute value of ๐ฅ plus one is greater than or equal to three โ we include the points where the graphs intersect.
00:01:04.600 --> 00:01:11.000
So we can say that one range of solutions are ๐ฅ-values that are greater than or equal to two.
00:01:11.920 --> 00:01:17.800
And the other range of solutions are ๐ฅ-values less than or equal to negative four.
00:01:18.760 --> 00:01:22.520
But remember, weโre looking to find a solution set.
00:01:23.040 --> 00:01:26.840
So how do we represent this using set notation?
00:01:28.400 --> 00:01:32.120
Well, weโre going to consider the inverse of what we just stated.
00:01:32.840 --> 00:01:42.800
We know that the values of ๐ฅ that donโt satisfy our inequality are the values of ๐ฅ from negative four to two, but not including negative four and two.
00:01:43.480 --> 00:01:47.520
So thatโs the open interval from negative four to two.
00:01:48.160 --> 00:01:57.680
And so the solution set of our inequality is the set of all real numbers minus the set of numbers in this open interval.
00:01:58.440 --> 00:02:08.040
So thatโs the set of all real numbers minus those in the open interval from negative four to two.