a Remember that greater than is represented by > and less than is represented by <.
B
b First, graph the inequalities separately to see the overlapping section clearly.
C
c Choose numbers from the red section, the blue section, and the overlapping section from Part B.
D
d Compare the colored sections in Part B and the numbers that satisfy the separate inequalities.
E
e What does the overlapping section in Part B represent?
A
aInequality I: x>4
Inequality II: x<9
B
b
C
c
Value of x
x>4
x<9
Both Are True
2
False
True
False
3
False
True
False
4
False
True
False
5
True
True
True
6
True
True
True
7
True
True
True
8
True
True
True
9
True
False
False
10
True
False
False
11
True
False
False
D
d See solution.
E
e See solution.
Practice makes perfect
a We are told that a number x is greater than 4 and the same number is less than 9. Let's write two separate inequalities for the statement.
Statements
Inequalities
x is greater than 4
x > 4
x is less than 9
x < 9
b Now, we can graph the inequalities from Part A on number lines and then highlight the overlapping section. Notice that, since the inequalities are strict, 4 and 9 are not included in the solution sets. Therefore, they will be represented with open circles.
Inequalities
Graphs
x > 4
x < 9
x > 4 and x < 9
c Let's make a table of values using ten numbers from the number lines in Part B.
Value of x
x>4
x<9
Both Are True
2
False
True
False
3
False
True
False
4
False
True
False
5
True
True
True
6
True
True
True
7
True
True
True
8
True
True
True
9
True
False
False
10
True
False
False
11
True
False
False
d The region on the number line where both graphs overlap and the values that are True in the Both Are True column correspond to the same numbers.
Graph
Table
Red region
True in the x>4 column
Intersection of both parts
True in both columns
Blue region
True in the x<9 column
The red region on the number line and the values that are True in the x>4 column also correspond to the same numbers. Lastly, the blue region on the number line and the values that are True in the x<9 column correspond to the same numbers as well.
e The solutions to the compound inequality 44 and x<9 at the same time. Notice that this corresponds to the overlapping section of the graphs of x>4 and x<9 in Part B.
Therefore we can predict that the graph of 44 and x<9 overlap.
