WEBVTT

1
00:00:00.000 --> 00:00:03.796
Here is the problem: |3x plus 9| equals 0.

2
00:00:04.247 --> 00:00:11.016
Solve an absolute value equation by splitting it into the cases where the inside is positive or negative.

3
00:00:11.816 --> 00:00:20.384
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
00:00:20.834 --> 00:00:24.874
An absolute value equals 0 only when its inside is 0.

5
00:00:25.324 --> 00:00:26.845
Solve the linear equation.

6
00:00:27.295 --> 00:00:30.035
Check each solution in the original equation.

7
00:00:30.835 --> 00:00:33.598
Write the solution set in interval notation.

8
00:00:34.398 --> 00:00:39.855
So the answer is x equals negative 3; interval notation: -3.

9
00:00:40.305 --> 00:00:49.024
An absolute value measures distance from zero, so |u| equals c means u is exactly c units from zero on either side.

10
00:00:49.824 --> 00:00:54.770
Substituting negative 3 gives 0 on the left, matching the right-hand side.