WEBVTT

1
00:00:00.000 --> 00:00:03.587
Here is the problem: |x minus 2| equals 1.

2
00:00:04.037 --> 00:00:10.515
Solve an absolute value equation by splitting it into the cases where the inside is positive or negative.

3
00:00:11.315 --> 00:00:20.394
Write the problem with the absolute value isolated. The absolute value is already alone on one side, so it can be split into cases.

4
00:00:20.844 --> 00:00:27.055
Split into two cases. The inside is either c units above zero or c units below zero.

5
00:00:27.505 --> 00:00:29.142
Solve the positive case.

6
00:00:29.592 --> 00:00:31.183
Solve the negative case.

7
00:00:31.983 --> 00:00:34.688
Check each solution in the original equation.

8
00:00:35.138 --> 00:00:37.797
Write the solution set in interval notation.

9
00:00:38.597 --> 00:00:44.541
So the answer is x equals 1 or x equals 3; interval notation: 1, 3.

10
00:00:44.991 --> 00:00:53.942
An absolute value measures distance from zero, so |u| equals c means u is exactly c units from zero on either side.

11
00:00:54.742 --> 00:00:59.328
Substituting 1 and 3 gives 1 on the left, matching the right-hand side.