>> Here are our answers. You've learned that inequalities have ranges of values
that are solutions to them. So that means that if a number falls in this range,
we can use it in the inequality to make a true statement. Some of these may be a
bit confusing though. For example, 3 is less than or equal to 7. On a number
line, if we're curious about all of the numbers that are less than or equal to
7, we would shade in all the numbers to the left of 7 on the number line. And
then draw a square bracket to include 7 in that range. We can see that 3
definitely falls in this region. It is not equal to 7, but it is less than 7.
And it only needs to fit one of the criteria implied by this symbol. It either
needs to be less than 7, or it needs to be equal to 7. Similarly, the statement
8 is greater than or equal to 1 plus 7 is also true. When simplified, this of
course gives us the inequality 8 is greater than or equal to 8. And you might at
first think, oh my gosh, 8 is not greater than 8. However it only needs to be
greater than or equal to 8. It's equal to 8 so that's enough to satisfy this
inequality. We can see the difference here then, between this symbol, the
greater than or equal to, which implies inclusion of 8, versus the just greater
than sign. This statement is true. Whereas this statement is not, because 8 is
greater than 1 plus 7, only allows for the greater than criterion, not the equal
to one. 1 plus 7 no longer fits the bill.