WEBVTT

1
00:00:00.000 --> 00:00:03.425
Here is the problem: x minus 5 less than 8.

2
00:00:03.875 --> 00:00:07.567
Solve the inequality and give the answer in interval notation.

3
00:00:08.367 --> 00:00:15.914
Move everything to one side and isolate the variable. Collect terms: x minus 13 less than 0.

4
00:00:16.364 --> 00:00:33.059
Test one point in each interval (sign chart). (-∞, 13): test x equals 12 → sign minus → included; (13, ∞): test x equals 14 → sign plus → excluded.

5
00:00:33.509 --> 00:00:36.632
Decide the endpoints. 13: excluded.

6
00:00:37.082 --> 00:00:38.580
Write the solution set.

7
00:00:39.380 --> 00:00:42.097
So the answer is (-∞, 13).

8
00:00:42.547 --> 00:00:58.174
The inequality holds exactly for x in (-∞, 13). 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
00:00:58.974 --> 00:01:02.492
x equals 12: satisfies the inequality.

10
00:01:02.942 --> 00:01:06.797
x equals 14: does not satisfy the inequality.