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Transcript
Graphing real numbers on the number line
(A) To graph the real numbers that are greater than or equal to 3 on a number line, we would
need to plot a point starting at 3 and on every single number to its right. This is practically an
impossible task. Instead, we only need to draw a solid dot on the 3 and draw a thick or bold line
to the right of 3, all the way to infinity (which we specify with an arrow head). So, if we let x
represent any real number, the corresponding graph for x ≥ 3 is:
-5 -4 -3 -2 -1
0 1
2
3
4
5
Suppose we now want all the numbers that are greater than 3, that is, not including the 3. Then
we use an open circle. The graph for x > 3 would be:
-5 -4 -3 -2 -1
0 1
2
3
4
5
Note:
Remember that the symbol ≥ is used for greater than or equal to, and the symbol > represents
greater than (that is, not including the given number).
(B) Let us now graph the real numbers that are less than or equal to 3 on a number line. Since
x ≤ 3,we want to include the 3 and we use a solid dot, like this:
-4
-3
-2
-1
0
1
2
3
4
5
The graph for x < 3 is shown next. Observe that we want the real numbers less that 3, but not
including the 3, thus the open circle.
-4
-3
-2
-1
0
1
2
3
4
5
Note:
Remember that the symbol ≤ is used for less than or equal to, and the symbol < represents less
than (that is, not including the given number).
Example 1
Write the inequality that corresponds to the given graph.
-5 -4 -3 -2 -1
0 1 2 3 4 5
Answer: x ≥ -5
Example 2
Choose the inequality that matches the given graph.
Page 1 of 3
-5 -4 -3 -2 -1
a. x > -2
0 1
2
3
4
b. x < -2
5
c. x > -1.5
d. x < -1.5
Answer: c
Example 3
Choose the graph that corresponds to the inequality x ≤ -2
a.
-5 -4 -3 -2 -1
0 1 2 3 4 5
-5 -4 -3 -2 -1
0 1
2
3
4
5
-5 -4 -3 -2 -1
0 1
2
3
4
5
b.
c.
d.
-5 -4 -3 -2 -1
0 1 2 3 4 5
Answer: a
Your turn to practice these problems!
(See Answer key on next page)
1. Use a number line to graph each of the following:
a. x ≤ -1
b. x ≥ -4
c. x < 4
d. x >0
e. x ≤ 0
2. Write the inequality that corresponds to the given graph.
a.
b.
-5 -4 -3 -2 -1
0 1
2
3
4
5
-5 -4 -3 -2 -1
0 1 2 3 4 5
Page 2 of 3
Answer Key for Practice Problems
1. a
-4
-3
-2
-1
0
1
2
3
4
5
3
4
5
3
4
5
3
4
5
3
4
5
b.
-5 -4 -3 -2 -1
0 1
2
c.
-4
-3
-2
-1
0
1
2
d.
-5 -4 -3 -2 -1
0 1
2
e.
-4
-3
-2
-1
0
1
2
2. a. x > -3.5
b. x ≤ 5
Page 3 of 3