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a.
Two separate inequalities for the given statement.
a.
![Check Mark](/static/check-mark.png)
Answer to Problem 54PPS
Explanation of Solution
Given:
A number x is greater than 4, and the same number is less than 9.
Calculation:
In order to write the inequalities for the given statement, observe that the number x is greater than 4, so in algebraic notation it can be written as,
Also given that the same number x is less than 9, so in algebraic notation it can be represented by the inequality as
Thus, the inequalities for the given statement are
b.
The graph of solution set by graphing the solution set of first inequality in red and solution set of second inequality in blue.
b.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
A number x is greater than 4, and the same number is less than 9.
Calculation:
The graph of the first inequality x > 4 is shown in red and the graph of the second inequality x < 9 is shown in blue. The region where they overlap is highlighted by green in the figure below,
c.
To make a table with ten points including points from each section.
c.
![Check Mark](/static/check-mark.png)
Answer to Problem 54PPS
x | Both are true | ||
1 | False | True | False |
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 |
Explanation of Solution
Given:
A number x is greater than 4, and the same number is less than 9.
Calculation:
The table is shown below,
x | Both are true | ||
1 | False | True | False |
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 |
d.
To describe the relationship between the colored regions of the graph and the chart.
d.
![Check Mark](/static/check-mark.png)
Explanation of Solution
Given:
A number x is greater than 4, and the same number is less than 9.
Calculation:
From the graph it is clear that the points between 4 and 9, excluding these points, satisfies both the inequalities. Also from the chart it is clear that the values between these two endpoints, both the inequalities holds true.
So, the colored region represents the solution of the combined inequalities.
Chapter 5 Solutions
Algebra 1
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