WEBVTT
00:00:01.030 --> 00:00:12.970
Determine the solution set of two π₯ plus five equals negative 11 using the substitution set negative 16, eight, negative eight, and one.
00:00:14.180 --> 00:00:29.210
To solve the equation two π₯ plus five equals negative 11, we could have used the balancing method and subtracted five from both sides of the equation then divided by two, and we would have got an answer of π₯ equals a number.
00:00:30.410 --> 00:00:34.080
However, in this case, weβre asked to use the substitution set.
00:00:34.580 --> 00:00:42.360
This means that we need to substitute negative 16, eight, negative eight, and one into our equation.
00:00:43.480 --> 00:00:50.580
Substituting in negative 16 gives us two multiplied by negative 16 plus five.
00:00:51.430 --> 00:00:55.080
Two multiplied by negative 16 is negative 32.
00:00:55.710 --> 00:01:00.520
And negative 32 plus five is equal to negative 27.
00:01:01.350 --> 00:01:07.550
As this is not equal to negative 11, then the solution set cannot contain negative 16.
00:01:08.790 --> 00:01:15.230
When we substitute eight into the equation, we get two multiplied by eight add five.
00:01:15.800 --> 00:01:17.740
Two multiplied by eight is 16.
00:01:18.040 --> 00:01:20.890
And 16 plus five is 21.
00:01:21.720 --> 00:01:25.400
Once again, 21 is not equal to negative 11.
00:01:25.710 --> 00:01:28.220
Therefore, eight is not in the solution set.
00:01:29.690 --> 00:01:31.780
Our third value was negative eight.
00:01:32.060 --> 00:01:37.850
When we substitute this in, we get two multiplied by negative eight plus five.
00:01:38.850 --> 00:01:42.020
Two multiplied by negative eight is negative 16.
00:01:42.330 --> 00:01:45.670
So we are left with negative 16 plus five.
00:01:46.410 --> 00:01:49.190
Well this does give us an answer of negative 11.
00:01:49.640 --> 00:01:54.030
Therefore, π₯ equals negative eight is in the solution set.
00:01:54.660 --> 00:02:01.180
Finally, substituting in π₯ equals one gives us two multiplied by one plus five.
00:02:01.930 --> 00:02:03.740
Two multiplied by one is two.
00:02:04.160 --> 00:02:06.590
And two plus five equals seven.
00:02:07.570 --> 00:02:11.690
Therefore, π₯ equals one is not in the solution set.
00:02:13.030 --> 00:02:30.170
As the only value that gave us an answer of negative 11 was negative eight, our solution set contains the value negative eight i.e., the solution set of two π₯ plus five equals negative 11 is negative eight.