1 00:00:00,012 --> 00:00:04,290 >> Here are our answers. You've learned that inequalities have ranges of values 2 00:00:04,290 --> 00:00:08,602 that are solutions to them. So that means that if a number falls in this range, 3 00:00:08,602 --> 00:00:12,840 we can use it in the inequality to make a true statement. Some of these may be a 4 00:00:12,840 --> 00:00:17,449 bit confusing though. For example, 3 is less than or equal to 7. On a number 5 00:00:17,449 --> 00:00:21,985 line, if we're curious about all of the numbers that are less than or equal to 6 00:00:21,985 --> 00:00:26,387 7, we would shade in all the numbers to the left of 7 on the number line. And 7 00:00:26,387 --> 00:00:30,630 then draw a square bracket to include 7 in that range. We can see that 3 8 00:00:30,630 --> 00:00:35,922 definitely falls in this region. It is not equal to 7, but it is less than 7. 9 00:00:35,922 --> 00:00:40,568 And it only needs to fit one of the criteria implied by this symbol. It either 10 00:00:40,568 --> 00:00:45,325 needs to be less than 7, or it needs to be equal to 7. Similarly, the statement 11 00:00:45,325 --> 00:00:49,809 8 is greater than or equal to 1 plus 7 is also true. When simplified, this of 12 00:00:49,809 --> 00:00:54,472 course gives us the inequality 8 is greater than or equal to 8. And you might at 13 00:00:54,472 --> 00:00:58,754 first think, oh my gosh, 8 is not greater than 8. However it only needs to be 14 00:00:58,754 --> 00:01:02,902 greater than or equal to 8. It's equal to 8 so that's enough to satisfy this 15 00:01:02,902 --> 00:01:07,106 inequality. We can see the difference here then, between this symbol, the 16 00:01:07,106 --> 00:01:11,528 greater than or equal to, which implies inclusion of 8, versus the just greater 17 00:01:11,528 --> 00:01:16,606 than sign. This statement is true. Whereas this statement is not, because 8 is 18 00:01:16,606 --> 00:01:22,150 greater than 1 plus 7, only allows for the greater than criterion, not the equal 19 00:01:22,150 --> 00:01:25,002 to one. 1 plus 7 no longer fits the bill.