WEBVTT 00:00:00.760 --> 00:00:03.370 Solve for x and check your solution. 00:00:03.370 --> 00:00:07.920 We have x divided by 3 is equal to 14. 00:00:07.920 --> 00:00:11.320 So to solve for x, to figure out what the variable x must 00:00:11.320 --> 00:00:14.135 be equal to, we really just have to isolate it 00:00:14.135 --> 00:00:15.760 on the left-hand side of this equation. 00:00:15.760 --> 00:00:16.884 It's already sitting there. 00:00:16.884 --> 00:00:19.490 We have x divided by 3 is equal to 14. 00:00:19.490 --> 00:00:24.960 We could also write this as 1/3 x is equal to 14. 00:00:24.960 --> 00:00:27.730 Obviously, x times 1/3 is going to be x/3. 00:00:27.730 --> 00:00:28.840 These are equivalent. 00:00:28.840 --> 00:00:31.800 So how can we just end up with an x on the left-hand side 00:00:31.800 --> 00:00:33.107 of either of these equations? 00:00:33.107 --> 00:00:34.440 These are really the same thing. 00:00:34.440 --> 00:00:36.370 Or another way, how can we just have a 1 00:00:36.370 --> 00:00:38.990 in front of the x, a 1x, which is really just saying 00:00:38.990 --> 00:00:40.650 x over here? 00:00:40.650 --> 00:00:42.860 Well, I'm dividing it by 3 right now. 00:00:42.860 --> 00:00:46.420 So if I were to multiply both sides of this equation by 3, 00:00:46.420 --> 00:00:47.680 that would isolate the x. 00:00:47.680 --> 00:00:50.100 And the reason that would work is if I multiply this 00:00:50.100 --> 00:00:54.140 by 3 over here, I'm multiplying by 3 and dividing by 3. 00:00:54.140 --> 00:00:55.310 That's equivalent. 00:00:55.310 --> 00:00:57.720 That's equivalent to multiplying or dividing by 1. 00:00:57.720 --> 00:00:58.995 These guys cancel out. 00:00:58.995 --> 00:01:00.870 Remember, if you do it to the left-hand side, 00:01:00.870 --> 00:01:03.004 you also have to do it to the right-hand side. 00:01:03.004 --> 00:01:04.879 And actually, I'll do both of these equations 00:01:04.879 --> 00:01:06.545 at the same time, because they're really 00:01:06.545 --> 00:01:08.470 the exact same equation. 00:01:08.470 --> 00:01:10.970 So what are we going to get over here on the left-hand side? 00:01:10.970 --> 00:01:15.350 3 times anything divided by 3 is going to be that anything. 00:01:15.350 --> 00:01:17.580 We're just going to have an x left over 00:01:17.580 --> 00:01:19.050 on the left-hand side. 00:01:19.050 --> 00:01:22.100 And on the right-hand side, what's 14 times 3? 00:01:22.100 --> 00:01:27.770 3 times 10 is 30, 3 times 4 is 12. 00:01:27.770 --> 00:01:29.510 So it's going to be 42. 00:01:29.510 --> 00:01:31.550 So we get x is equal to 42. 00:01:31.550 --> 00:01:33.120 And the same thing would happen here. 00:01:33.120 --> 00:01:36.250 3 times 1/3 is just 1. 00:01:36.250 --> 00:01:39.820 So you get 1x is equal to 14 times 3, which is 42. 00:01:39.820 --> 00:01:41.250 Now let's just check our answer. 00:01:41.250 --> 00:01:44.060 Let's substitute 42 into our original equation. 00:01:44.060 --> 00:01:52.190 So we have 42 in place for x over 3 is equal to 14. 00:01:52.190 --> 00:01:54.370 So what's 42 divided by 3? 00:01:54.370 --> 00:01:57.210 And we could do a little bit of-- I guess we call it 00:01:57.210 --> 00:01:58.200 medium-long division. 00:01:58.200 --> 00:01:59.690 It's not really long division. 00:01:59.690 --> 00:02:01.210 3 into 4. 00:02:01.210 --> 00:02:02.580 3 goes into 4 one time. 00:02:02.580 --> 00:02:04.370 1 times 3 is 3. 00:02:04.370 --> 00:02:05.250 You subtract. 00:02:05.250 --> 00:02:07.100 4 minus 3 is 1. 00:02:07.100 --> 00:02:08.370 Bring down the 2. 00:02:08.370 --> 00:02:13.110 3 goes into 12 four times. 00:02:13.110 --> 00:02:14.710 3 goes into 42 14 times. 00:02:14.710 --> 00:02:19.230 So this right over here simplifies to 14. 00:02:19.230 --> 00:02:22.640 And it all checks out, so we're done.