Student: _____________________
Date: _____________________
Instructor: Roxberg Laura
Course: Algebra II
Assignment: 1.1­1.5 Review for test
1. Classify the variable according to the set of numbers that best describes its values.
the temperature t measured to the nearest degree Celsius
Choose the correct answer below.
integers
natural numbers
rational numbers
irrational numbers
2. Compare the two numbers. Use > or < .
4.4, 26
Select the correct inequality symbol.
4.4 (1) 26
(1) >
<
3. Solve the equation.
w − 9 = 1.3
w=
(Simplify your answer. Type an integer or a decimal.)
4. Solve the equation for k.
6k − 2z = 12
k=
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
5. Solve the equation.
−
x
3
= 26
x=
(Simplify your answer.)
6. Solve the equation.
7 − (x + 6) = 5x − 5
The solution is x =
.
7. Solve the formula for the indicated variable.
W = XYZ for Z Z=
8. Solve for h.
A=
7 3 The solution is h =
A+
.
(Simplify your answers. Type an integer or a fraction.)
(h − 58)
9. Solve the equation.
25 − 3(2w + 1) = 10w − 3(10 + w)
w=
(Simplify your answer.)
10. Solve the formula for the indicated variable.
S(r + t) = rt, for t
t=
(Simplify your answer.)
11. Solve the following inequality. Graph the solution.
6a − 27 > 33
What is the solution? Select the correct choice below and fill in the answer box within your choice.
(Type an integer or a decimal.)
A. a <
B. a ≤
C. a >
D. a ≥
Choose the correct graph below.
A.
C.
E.
G.
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
B.
D.
F.
H.
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
­15 ­12 ­9
­6 ­3
0
3
6
9
12 15
12. Solve the inequality. Graph the solution.
3(m − 6) + 5 < 20
What is the solution?
m (1) Choose the correct graph below.
A.
0
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
B.
C.
D.
(1) <
>
13. Solve the inequality. Graph the solution.
− 2(w + 6) + 8 < − 18
What is the solution? Select the correct choice below and fill in the answer box within your choice.
(Type an integer or a decimal.)
A. w <
B. w ≥
C. w ≤
D. w >
Choose the correct graph below.
A.
C.
E.
G.
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
B.
D.
F.
H.
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
­15 ­12 ­9 ­6 ­3
0
3
6
9
12 15
14. Is the inequality always, sometimes, or never true?
4x − 5 < 4(x − 3)
Choose the correct answer below.
Sometimes true
Never true
Always true
15. Is the inequality always, sometimes, or never true?
5x − 24 < 5(x − 5)
Choose the correct answer below.
Sometimes true
Always true
Never true
16. Solve the following compound inequality. Graph the solution.
8x ≤ − 48 or 4x ≥ 20
What is the solution? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
A. x ≤
(Type an integer or a decimal.)
B. x ≥
(Type an integer or a decimal.)
C. x ≤
or x ≥
D.
(Type integers or decimals.)
≤x≤
(Type integers or decimals.)
E. The compound inequality has no solution.
F. The solution is all real numbers.
Choose the correct graph of the solution below.
A.
C.
E.
G.
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
B.
D.
F.
H.
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
17. Solve the following compound inequality. Graph the solution.
4x ≥ − 24 and 8x ≤ 24
What is the solution? Select the correct answer below and, if necessary, fill in the answer boxes within your choice.
A. x ≤
or x ≥
B. x ≤
(Type an integer or a decimal.)
C. x ≥
(Type an integer or a decimal.)
D.
(Type integers or decimals.)
≤x≤
(Type integers or decimals.)
E. The compound inequality has no solution.
F. The solution is all real numbers.
Choose the correct graph of the solution below.
A.
C.
E.
G.
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
18. Solve the equation. Check your answer.
− 5x = 45
B.
D.
F.
H.
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
­10 ­8 ­6 ­4 ­2
0
2
4
6
8
10
x = (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
19. Solve the equation. Check for extraneous solutions.
x − 2 = 5x + 6
x=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
20. Solve.
4x = 8
21. Solve the equation. Check your answer.
− 2x = 14
x = (Simplify your answer. Type an integer or a fraction. Use commas to separate answers as needed.)
x = (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.)
22. Solve the equation. Check your answers.
3 3x − 2 = 30
x=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
23. Solve the equation. Check for extraneous solutions.
x − 3 = 5x + 13
x=
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
24. Solve the inequality. Graph the solution.
7x − 7 + 4 < 25
What is the solution?
(Type an inequality or a compound inequality.)
Choose the correct graph below.
A.
­10
­5
0
5
10
­10
­5
0
5
10
­10
­5
0
5
10
­10
­5
0
5
10
B.
C.
D.
25. Solve the inequality. Graph the solution.
3x − 3 + 1 < 10
What is the solution?
(Type an inequality or a compound inequality.)
Choose the correct graph below.
A.
­10
­5
0
5
10
­10
­5
0
5
10
­10
­5
0
5
10
­10
­5
0
5
10
B.
C.
D.
26. Solve the inequality. Graph the solution.
Solve the inequality. Select the correct choice below and fill in the answer boxes within your choice.
|x + 16| > 7
A.
x<
or x>
<x<
B.
C. The solution is all real numbers.
D. There is no solution.
Choose the correct graph below.
A.
B.
C.
­40 ­35 ­30 ­25 ­20 ­15 ­10
­5
0
­40 ­35 ­30 ­25 ­20 ­15 ­10
­5
0
­40 ­35 ­30 ­25 ­20 ­15 ­10
­5
0
D. The graph contains no points.
27. Solve the inequality. Graph the solution.
2x + 2 ≥ − 10
Solve the inequality. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. x ≤
or x ≥
B.
≤x≤
C. The solution is all real numbers.
D. There is no solution.
Choose the correct graph below.
A.
­6
­10
C.
0
­6
­10
B.
4
10
0
D. The graph contains no points.
4
0
­10
10
10
28. Solve the inequality. Graph the solution.
4x + 2 − 15 ≤ − 9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution is . (Type an inequality or a compound inequality. Use integers or fractions for any numbers in the expression.)
B. The solution is all real numbers.
C. There is no solution.
Choose the correct graph below.
A.
B.
­15
0
15
C.
­15
0
15
­15
0
15
D.
­15
0
15
E.
F. The graph contains no points.
­15
0
15
1. integers
2. (1) <
3. 10.3
4.
2+
1
3
z
5. − 78
6. 1
7. W
XY
8. 3
7
58
9. 4
10.
Sr
r− S
11. C. a >
10
F. ­15­12 ­9 ­6 ­3 0 3 6 9 12 15
12. (1) <
11
D. 0
5
13. D. w >
7
10
15
B. ­15­12 ­9 ­6 ­3 0 3 6 9 12 15
14. Never true
15. Never true
16. C. x ≤
−6
or x ≥
5
(Type integers or decimals.)
C. ­10 ­8 ­6 ­4 ­2 0 2 4 6 8 10
17. D. −6
≤x≤
3
(Type integers or decimals.)
B. ­10 ­8 ­6 ­4 ­2 0 2 4 6 8 10
18. − 9,9
19.
−
2
3
20. − 2,2
21. − 7,7
22.
23.
4, −
−
8
3
5
3
24. − 2 < x < 4
A. ­10
­5
0
5
10
­5
0
5
10
25. − 2 < x < 4
C. ­10
26. A. x <
− 23
or x >
−9
A. ­40 ­35 ­30 ­25 ­20 ­15 ­10 ­5 0
27. C. The solution is all real numbers.
B. ­10
0
28. A. The solution is 10
−2≤x≤1
. (Type an inequality or a compound inequality. Use integers or fractions for any numbers in the expression.)
A. ­15
0
15