WEBVTT

1
00:00:00.000 --> 00:00:07.802
Here is the problem: negative 2x squared minus 20x minus 48 greater than equals 0.

2
00:00:08.252 --> 00:00:11.874
Solve the inequality and give the answer in interval notation.

3
00:00:12.674 --> 00:00:21.881
Move everything to one side and factor. A sign chart needs the form f(x) compared with 0, written as a product/quotient of factors.

4
00:00:22.331 --> 00:00:27.939
Find the critical points. The sign can only change at negative 6 (zero), negative 4 (zero).

5
00:00:28.389 --> 00:00:52.909
Test one point in each interval (sign chart). (-∞, negative 6): test x equals negative 7 → sign minus → excluded; (negative 6, negative 4): test x equals negative 5 → sign plus → included; (negative 4, ∞): test x equals negative 3 → sign minus → excluded.

6
00:00:53.359 --> 00:01:06.072
Decide the endpoints. negative 6: included (the expression equals 0 and the sign allows equality); negative 4: included (the expression equals 0 and the sign allows equality).

7
00:01:06.872 --> 00:01:08.370
Write the solution set.

8
00:01:09.170 --> 00:01:11.852
So the answer is [-6, negative 4].

9
00:01:12.302 --> 00:01:27.395
The inequality holds exactly for x in [-6, negative 4]. 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.

10
00:01:28.195 --> 00:01:32.468
x equals negative 7: does not satisfy the inequality.

11
00:01:32.918 --> 00:01:36.877
x equals negative 5: satisfies the inequality.

12
00:01:37.327 --> 00:01:41.727
x equals negative 3: does not satisfy the inequality.