WEBVTT

1
00:00:00.000 --> 00:00:05.201
Here is the problem: 2x squared plus 5x minus 3 greater than 0.

2
00:00:05.651 --> 00:00:09.320
Solve the inequality and give the answer in interval notation.

3
00:00:10.120 --> 00:00:19.199
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
00:00:19.649 --> 00:00:25.384
Find the critical points. The sign can only change at negative 3 (zero), 1 over 2 (zero).

5
00:00:25.834 --> 00:00:50.761
Test one point in each interval (sign chart). (-∞, negative 3): test x equals negative 4 → sign plus → included; (negative 3, 1 over 2): test x equals negative 1.25 → sign minus → excluded; (1 over 2, ∞): test x equals 2 → sign plus → included.

6
00:00:51.211 --> 00:00:57.016
Decide the endpoints. negative 3: excluded; 1 over 2: excluded.

7
00:00:57.816 --> 00:00:59.267
Write the solution set.

8
00:01:00.067 --> 00:01:04.769
So the answer is (-∞, negative 3) ∪ (1 over 2, ∞).

9
00:01:05.219 --> 00:01:21.148
The inequality holds exactly for x in (-∞, negative 3) ∪ (1 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.

10
00:01:21.948 --> 00:01:25.872
x equals negative 4: satisfies the inequality.

11
00:01:26.322 --> 00:01:31.303
x equals negative 1.25: does not satisfy the inequality.

12
00:01:31.753 --> 00:01:35.166
x equals 2: satisfies the inequality.