WEBVTT
00:00:00.440 --> 00:00:07.270
Find the solution set of π₯ over four minus three equals negative five in the set of all integers.
00:00:08.090 --> 00:00:12.010
First, we remember that this symbol is the set of all integers.
00:00:12.610 --> 00:00:15.460
And then, we can turn our attention to solving for π₯.
00:00:15.840 --> 00:00:23.810
If π₯ over four minus three equals negative five, we want to try to isolate π₯, to get π₯ by itself.
00:00:24.320 --> 00:00:29.820
And the first thing we should do in order to do that is add three to both sides.
00:00:30.720 --> 00:00:38.700
Once we do that, weβll get π₯ over four is equal to negative two because negative five plus three equals negative two.
00:00:39.420 --> 00:00:43.010
We know that π₯ over four means π₯ divided by four.
00:00:43.290 --> 00:00:46.460
Some value divided by four equals negative two.
00:00:46.770 --> 00:00:50.890
To find out what that value is, we need to do the opposite.
00:00:51.090 --> 00:00:58.220
If π₯ is being divided by four, we need to multiply both sides of the equation by four, like this.
00:00:58.850 --> 00:01:05.650
Four times π₯ over four equals π₯, and negative two times four equals negative eight.
00:01:06.160 --> 00:01:08.480
At this point, we should check and see if thatβs true.
00:01:09.030 --> 00:01:13.310
Is negative eight divided by four minus three equal to negative five?
00:01:13.830 --> 00:01:17.690
Negative eight divided by four is negative two.
00:01:18.590 --> 00:01:22.310
And negative two minus three is negative five.
00:01:22.830 --> 00:01:25.450
This means that π₯ is equal to negative eight.
00:01:25.770 --> 00:01:29.920
But here our solution needs to be given as a set notation.
00:01:30.280 --> 00:01:31.790
Thatβs the curly brackets.
00:01:32.270 --> 00:01:36.520
And the solution set for this equation is just negative eight.