Solving Equations Examples And Worksheet Page 12
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14A60
Appendix A
Review of Fundamental Concepts of Algebra
A.5
EXERCISES
See for worked-out solutions to odd-numbered exercises.
VOCABULARY:
Fill in the blanks.
1. A(n) ________ is a statement that equates two algebraic expressions.
2. A linear equation in one variable is an equation that can be written in the standard form ________.
3. When solving an equation, it is possible to introduce an ________ solution, which is a value that does not
satisfy the original equation.
4. The four methods that can be used to solve a quadratic equation are ________, ________, ________, and the ________.
SKILLS AND APPLICATIONS
In Exercises 5–12, determine whether the equation is an
2
1
2
33.
3
2
34.
0
identity or a conditional equation.
z
2
x
x
5
x
4
5.
4 x
1
4x
4
35.
2
0
x
4
x
4
6.
2 x
3
7x
1
7
8x
7.
6 x
3
5
2x
10
36.
4
2x
1
2x
1
8.
3 x
2
5
3x
1
2
1
2
9.
4 x
1
2x
2 x
2
37.
x
4 x
2
x
4
x
2
2
2
10.
x
2 3x
2
x
6x
4
1
3
4
1
4x
5
3
38.
11.
3
12.
24
2
x
2
x
3
x
x
6
x
1
x
1
x
x
3
4
1
6
2
3 x
5
39.
40.
In Exercises 13–26, solve the equation and check your
2
2
x
3x
x
x
3
x
x
3
x
3x
solution.
2
2
41.
x
2
5
x
3
13.
x
11
15
14.
7
x
19
2
2
42.
2x
1
4 x
x
1
15.
7
2x
25
16.
7x
2
23
In Exercises 43– 46, write the quadratic equation in general
17.
8x
5
3x
20
18.
7x
3
3x
17
form.
19.
4y
2
5y
7
6y
2
2
43.
2x
3
8x
44.
13
3 x
7
0
20.
3 x
3
5 1
x
1
1
2
2
45.
3x
10
18x
46.
x x
2
5x
1
5
21.
x
3 2x
3
8
5x
22.
9x
10
5x
2 2x
5
In Exercises 47– 58, solve the quadratic equation by factoring.
x
x
3x
3x
4x
2
2
47.
6x
3x
0
48.
9x
4
0
23.
4
24.
3
8
3
5
2
10
2
2
49.
x
2x
8
0
50.
x
10x
9
0
3
1
25.
z
5
z
24
0
2
4
2
2
51.
x
12x
35
0
52.
4x
12x
9
0
26.
0.60x
0.40 100
x
50
2
2
53.
3
5x
2x
0
54.
2x
19x
33
1
2
2
55.
x
4x
12
56.
x
x
16
0
In Exercises 27–42, solve the equation and check your
8
solution. (If not possible, explain why.)
2
2
57.
x
2ax
a
0,
a
is a real number
2
2
58.
x
a
b
0,
a
and are real numbers
b
27.
x
8
2 x
2
x
28.
8 x
2
3 2x
1
2 x
5
In Exercises 59–70, solve the equation by extracting square roots.
100
4x
5x
6
29.
6
2
2
59.
x
49
60.
x
32
3
4
2
2
61.
3x
81
62.
9x
36
17
y
32
y
30.
100
2
2
63.
x
12
16
64.
x
13
25
y
y
2
2
65.
x
2
14
66.
x
5
30
5x
4
2
15
6
31.
32.
4
3
2
2
67.
2x
1
18
68.
2x
3
27
0
5x
4
3
x
x
2
2
2
2
69.
x
7
x
3
70. x
5
x
4
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