WEBVTT

1
00:00:00.000 --> 00:00:04.481
Here is the problem: negative 2x minus 3 greater than 0.

2
00:00:04.931 --> 00:00:08.576
Solve the inequality and give the answer in interval notation.

3
00:00:09.377 --> 00:00:21.556
Move everything to one side and isolate the variable. Collect terms: negative 2x minus 3 greater than 0. Dividing by a negative coefficient reverses the inequality sign.

4
00:00:22.006 --> 00:00:40.419
Test one point in each interval (sign chart). (-∞, negative 3 over 2): test x equals negative 3 → sign plus → included; (negative 3 over 2, ∞): test x equals 0 → sign minus → excluded.

5
00:00:40.869 --> 00:00:44.944
Decide the endpoints. negative 3 over 2: excluded.

6
00:00:45.394 --> 00:00:46.892
Write the solution set.

7
00:00:47.692 --> 00:00:51.279
So the answer is (-∞, negative 3 over 2).

8
00:00:51.729 --> 00:01:08.505
The inequality holds exactly for x in (-∞, negative 3 over 2). 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
00:01:09.305 --> 00:01:13.496
x equals negative 3: satisfies the inequality.

10
00:01:13.946 --> 00:01:17.568
x equals 0: does not satisfy the inequality.