Linear Equations And Inequalities In One Variable Worksheet With Answer Key Page 5
ADVERTISEMENT
1
2
3
4
5
6
7
8124
(2-60)
Chapter 2 Linear Equations and Inequalities in One Variable
It is customary to write 8
x
0 with the smallest number on the left:
0
x
8
– 1
0
1
2
3
4
5
6
7
8
9
F I G U R E 2 . 1 6
Figure 2.16 shows all numbers that satisfy
3
5
x
5.
Applications of Inequalities
The following example shows how inequalities can be used in applications.
E X A M P L E
6
Averaging test scores
Mei Lin made a 76 on the midterm exam in history. To get a B, the average of her
midterm and her final exam must be between 80 and 90. For what range of scores
on the final exam will she get a B?
Solution
x
76
Let x represent the final exam score. Her average is then
. The inequality
h e l p f u l
h i n t
2
expresses the fact that the average must be between 80 and 90:
Remember that all inequality
x
76
symbols in a compound in-
80
90
equality must point in the
2
same direction. We usually
x
76
have them all point to the left
2(80)
2
2(90)
Multiply each part by 2.
so that the numbers are in-
2
creasing in size as you go from
160
x
76
180
Simplify.
left to right in the inequality.
160
76
x
76
76
180
76
Subtract 76 from each part.
84
x
104
Simplify.
The last inequality indicates that Mei Lin’s final exam score must be between 84
and 104.
W A R M - U P S
True or false? Explain your answer.
1. The inequality 2x
18 is equivalent to x
9.
True
2. The inequality x
5
0 is equivalent to x
5.
False
3. We can divide each side of an inequality by any real number.
False
4. The inequality
2x
6 is equivalent to
x
3.
True
5. The statement “x is at most 7” is written as x
7.
False
6. “The sum of x and 0.05x is at least 76” is written as x
0.05x
76.
True
7. The statement “x is not more than 85” is written as x
85.
False
8. The inequality
3
x
9 is equivalent to
9
x
3.
True
9. If x is the sale price of Glen’s truck, the sales tax rate is 8%, and the title fee
is $50, then the total that he pays is 1.08x
50 dollars.
True
10. If the selling price of the house, x, less the sales commission of 6% must be
at least $60,000, then x
0.06x
60,000.
False
ADVERTISEMENT
0 votes
Related Articles
Related forms
Graphs, Linear Equations, And Inequalities In Two Variables, Functions Worksheet - Mat 100, Armstrong/pierson
Education
Linear Equations/two Variable Worksheet With Answer Key - Ann Padden, Joliet Junior College
Education
Related Categories
Parent category: Education