WEBVTT

1
00:00:00.000 --> 00:00:05.375
Here is the problem: 2x(3 plus x) equals 2x squared plus 12.

2
00:00:05.825 --> 00:00:10.539
A linear equation in x: isolate x using inverse operations.

3
00:00:11.339 --> 00:00:12.837
Start with the equation.

4
00:00:13.287 --> 00:00:15.458
Collect all terms on one side.

5
00:00:15.908 --> 00:00:16.965
Isolate x.

6
00:00:17.765 --> 00:00:21.457
Now look at the graph of the left side minus the right side.

7
00:00:21.907 --> 00:00:25.657
It crosses zero exactly at the solutions we found.

8
00:00:26.457 --> 00:00:28.756
So the answer is x equals 2.

9
00:00:29.206 --> 00:00:38.389
Doing the same operation to both sides keeps the equation balanced. Undoing addition, then multiplication, leaves x alone.

10
00:00:39.189 --> 00:00:45.633
x equals 2: left side equals 20, right side equals 20, which checks out.