MathB65
Chapter 1 Homework
Part I Algebraic Expressions
Evaluate the given expression for the given value of the variable.
1) + 5; = 7
2) 2 ; = 5
3) 7 + 2; = 5
4)
+ 3; = 6
5) 4 +
;
= −2
Simplify each algebraic expression.
6) 10 + 8
7) 3 − 8 + 1
8)
+
−7
9) 3( + 2) + 4
10) 2( + 2) + 3( + 1)
11) 3( − 4) − 2( − 1)
Part II Translations
12) The sum of five and a number
13) The product of a number and 10
14) The difference of 10 and a number
Part III Introduction to Equations
Determine if the given number is a solution to the equation.
15) 2 + 1 = 7; = 2
16) 3 − = 7; = −4
17)
+ 5 = 9;
=6
18) 3( + 2) − 5 = 2 ;
= −1
Translate the English sentence into an equation.
19) If twelve is subtracted from a number the answer is 14.
20) The product of 5 and a number is .
21) The sum of 5 and twice a number is 17.
22) The difference between and 8 is of that number.
Part IV The Addition and Multiplication Properties
Solve the following equations.
23) − 10 = 21
24) −3 = + 7
25) + = 2
26) 5 = 15
27) −49 = 7
28) −3 = 10
29) = 6
30)
=5
31) − = 10
32) + = −
Part V Strategy to Solve Linear Equations in One Variable
33) 2 − 1 = 5
34) 7 − 9 = 12
35) 3( − 2) = 6
36) 5 + 9 − 7 + 6 = + 18
37) 3( + 4) = 5 − 12
38) 1 − 2(6 − ) = 3 + 2
39) 3(8 − 1) = 6(5 + 4 )
40) 4(2 − 3) + 4 = 8 − 8
Part VI Formulas
Solve the following formulas for the indicated variable.
41) =
42) =
; solve for
ℎ solve for h
43)
44) 3
45) 6
46)
= 2 + 2 solve for l
+ 4 = 5 solve for y
− 2 = 8 solve for y
+
= solve for y
47)
=
solve for C
48)
=
+ 32 solve for C
Part VII Problem Solving
49) In 2003, the average weekly salary for workers in the United States was $612. If this
amount is increasing by $15 yearly, in how many years after 2003 will the average salary
reach $747? In which year will that be?
50) A rectangular field is three times as long as it is wide. If the perimeter of the field is 400
yards, what are the field’s dimensions?
Parts VIII and IX Linear Inequalities
Solve each problem. Express the answer in both set-builder notation and interval notation.
51) 2 − 5 < 3
52)
> −4
53) 3 − 5 ≤ 18
54) 4 + 6 < 5
55) 6 − 10 ≥ 2( + 3)
56) 4 + 3(2 − 7) ≤ − 3
57) 2(2 + 4) > 4( + 2) − 6
58) −2( − 4) ≤ 3 + 1 − 5
59) To pass a course, a student must have an average on three examinations of at least 60. If a
student scores 42 and 74 on the first two tests, what must be earned on the third test to
pass the course?
Part X Intersections and Unions
Find
60)
61)
62)
∪
and
∩
for the following sets.
= , , , , and
= 2,4,6,8,10 and
= 2,4,6,8,10 and
= , , , ,
= 1,2,3,4, ,5
= 1,3,5,7,9
Graph and write the following sets in interval notation
63)
64)
| > 3 or < −2
| < 3 and > −2
65)
>
or
66)
>
and
<
> −2
Solve the following compound inequalities. Give your answer in both set-builder and interval
notation.
67) −3 < 4 and 2 < 14
68)
+ 1 < 4 or 2 + 1 ≥ −9
69) 7 + 4 < −5 + and 2 + 10 < −2
70) 6.2 − 1.1 ≤ 1 or 1.2 − 4 ≥ 2.7
71) −4 ≤ 2 + 1 < 6