﻿[Script Info] Title: [Events] Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text Dialogue: 0,0:00:00.01,0:00:04.29,Default,,0000,0000,0000,,&gt;&gt; Here are our answers. You've learned that inequalities have ranges of values Dialogue: 0,0:00:04.29,0:00:08.60,Default,,0000,0000,0000,,that are solutions to them. So that means that if a number falls in this range, Dialogue: 0,0:00:08.60,0:00:12.84,Default,,0000,0000,0000,,we can use it in the inequality to make a true statement. Some of these may be a Dialogue: 0,0:00:12.84,0:00:17.45,Default,,0000,0000,0000,,bit confusing though. For example, 3 is less than or equal to 7. On a number Dialogue: 0,0:00:17.45,0:00:21.98,Default,,0000,0000,0000,,line, if we're curious about all of the numbers that are less than or equal to Dialogue: 0,0:00:21.98,0:00:26.39,Default,,0000,0000,0000,,7, we would shade in all the numbers to the left of 7 on the number line. And Dialogue: 0,0:00:26.39,0:00:30.63,Default,,0000,0000,0000,,then draw a square bracket to include 7 in that range. We can see that 3 Dialogue: 0,0:00:30.63,0:00:35.92,Default,,0000,0000,0000,,definitely falls in this region. It is not equal to 7, but it is less than 7. Dialogue: 0,0:00:35.92,0:00:40.57,Default,,0000,0000,0000,,And it only needs to fit one of the criteria implied by this symbol. It either Dialogue: 0,0:00:40.57,0:00:45.32,Default,,0000,0000,0000,,needs to be less than 7, or it needs to be equal to 7. Similarly, the statement Dialogue: 0,0:00:45.32,0:00:49.81,Default,,0000,0000,0000,,8 is greater than or equal to 1 plus 7 is also true. When simplified, this of Dialogue: 0,0:00:49.81,0:00:54.47,Default,,0000,0000,0000,,course gives us the inequality 8 is greater than or equal to 8. And you might at Dialogue: 0,0:00:54.47,0:00:58.75,Default,,0000,0000,0000,,first think, oh my gosh, 8 is not greater than 8. However it only needs to be Dialogue: 0,0:00:58.75,0:01:02.90,Default,,0000,0000,0000,,greater than or equal to 8. It's equal to 8 so that's enough to satisfy this Dialogue: 0,0:01:02.90,0:01:07.11,Default,,0000,0000,0000,,inequality. We can see the difference here then, between this symbol, the Dialogue: 0,0:01:07.11,0:01:11.53,Default,,0000,0000,0000,,greater than or equal to, which implies inclusion of 8, versus the just greater Dialogue: 0,0:01:11.53,0:01:16.61,Default,,0000,0000,0000,,than sign. This statement is true. Whereas this statement is not, because 8 is Dialogue: 0,0:01:16.61,0:01:22.15,Default,,0000,0000,0000,,greater than 1 plus 7, only allows for the greater than criterion, not the equal Dialogue: 0,0:01:22.15,0:01:25.00,Default,,0000,0000,0000,,to one. 1 plus 7 no longer fits the bill.