WEBVTT

1
00:00:00.000 --> 00:00:04.725
Here is the problem: negative 6x minus 6 less than 7.

2
00:00:05.175 --> 00:00:08.879
Solve the inequality and give the answer in interval notation.

3
00:00:09.679 --> 00:00:21.881
Move everything to one side and isolate the variable. Collect terms: negative 6x minus 13 less than 0. Dividing by a negative coefficient reverses the inequality sign.

4
00:00:22.331 --> 00:00:40.535
Test one point in each interval (sign chart). (-∞, negative 13 over 6): test x equals negative 4 → sign plus → excluded; (negative 13 over 6, ∞): test x equals negative 1 → sign minus → included.

5
00:00:40.985 --> 00:00:45.246
Decide the endpoints. negative 13 over 6: excluded.

6
00:00:45.696 --> 00:00:47.217
Write the solution set.

7
00:00:48.017 --> 00:00:51.895
So the answer is (negative 13 over 6, ∞).

8
00:00:52.345 --> 00:01:07.032
The inequality holds exactly for x in (negative 13 over 6, ∞). Points where the expression is undefined are never included, and endpoints are included only for less than or equal to or greater than or equal to where the expression equals zero.

9
00:01:07.832 --> 00:01:12.162
x equals negative 4: does not satisfy the inequality.

10
00:01:12.612 --> 00:01:16.490
x equals negative 1: satisfies the inequality.