Welcome to several examples of comparing integers. We'll perform the comparisons
using the number line. We are told to
select the correct inequality symbol for
each of the following pairs of numbers.
Let's first look at the number line
below. Positive integers are always to the
right of 0. Negative integers always to
the left of zero. When comparing two
numbers on the number line, the number on
the left is always less than the number
on the right. And the number on the right
is always greater than the number on the
left We want to begin by comparing
negative 7 to 0. Let's plot these two
integers on the number line. 0 is located
her. Negative 7 is 7 units to the left
of zero. So if we scale the number line
by ones, we have negative 1 negative 2
and so on.
Negative 7 is located here. Because we're
comparing negative 7 to 0 and negative 7
is to the left of 0,
this indicates negative 7 is less than
zero. And Therefore we enter the less
than inequality symbol.  Notice how the
inequality symbol points toward the
smaller integer. Next we compare positive
4 to negative 7. Using the same number
line, let's erase the plot  for 0 and plot
positive 4. Positive 4 is located
four units to the right of zero. So now
we have negative 7 and positive 4
plotted on the number line. Because we're
comparing positive 4 to negative 7 and
positive 4 is to the right of negative
7,
this indicates positive 4 is greater
than negative 7. We enter the greater
than inequality symbol. For the next
comparison, we need to compare negative
3143 to negative 2393. To plot these values on the number line, let's scale the number
line by thousands to the left of zero. We
have negative 1,000 negative two
thousand negative three thousand and
negative four thousand. And now let's
plot negative 3143 which is 3143 units
to the left of 0, which is approximately
here.
Now we plot negative 2393, which is 2393
units to the left of 0, which is located
approximately here. Notice that negative
3143 is to the left of negative 2393,
which means negative 3143 is less than
negative 2393. We enter the less than
inequality symbol. Next we need to
compare a negative 1 to  negative 3. We will
scale the number line by ones to the
left of 0. Negative 1 negative 2 negative
3 negative 4. Plot negative 1, plot
negative 3.
We're comparing negative 1 to negative 3.
Notice negative 1 is to the right of
negative 3, which means negative 1 is
greater than negative 3. We enter the
greater than inequality symbol. Next we
compare positive 3 to negative 3. We
should recognize any positive integer
it's going to be greater than a negative
integer, but let's go ahead and plot the
integers on the number line. Using this
number line we'll erase the plot on
negative 1, use a plot of negative 3, and
now plot positive 3. Positive 3 is 3
units to the right of zero. So here is
positive 3.
We're comparing positive 3 to negative 3.
Positive 3 is to the right of negative 3,
which indicates positive 3 is greater
than negative 3.  For the last comparison
we compare negative 30 to  negative 31 To plot these values
let's scale the axis by tens to the left
of 0.  Negative 10 negative 20 and
negative 30.
First plot negative 30, which is 30 units
to the left of zero, located here.
Negative 31 is 31 units to the left of 0,
which is just to the left of negative 3.
Let's say approximately here. We are
comparing negative 30 to negative 31.
Because negative 30 is to the right of
negative 31, negative 30 is greater than
negative 31.
I hope you found this helpful.
