Download Linear Inequalities

Study Island
Copyright © 2015 Edmentum - All rights reserved.
Generation Date: 02/22/2015
Generated By: Robert Dilliplane
1. Which of the following number lines shows the solution to the compound inequality given
below?
-8 < 2x + 2 < 12
A.
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
B.
C.
D.
2. Which of the following graphs shows the solution set for the inequality below?
|x + 2| + 9 > 12
A.
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
B.
C.
D.
3. Solve the following inequality.
A.
B.
C.
D.
4. Which of the following compound inequalities is graphed below?
-6
A. x < -3 AND x > 2
B. x < -3 OR x > 2
C. x < -3 OR x > 2
D. x < -3 AND x > 2
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
5. Which of the following graphs shows the solution set for the inequality below?
2|x - 1| > 6
A.
-2
-1
0
1
2
3
4
5
6
7
8
9
10
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
B.
C.
D.
6. Which of the following number lines shows the solution to the inequality given below?
5x - 7 < -27 OR 3x - 3 > 6
A.
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
B.
C.
D.
7. Solve the following compound inequality.
-5x + 8 < 43 AND 5x - 4 < 16
A. -8 < x < 4
B. x < -7 AND x > 4
C. x < 4
D. -7 < x < 4
8. Solve the following compound inequality.
5x - 4 > 11 OR -2x < -14
A. x < 3 OR x > 7
B. x > 3
C. 3 < x < 7
D. x > 7
9. The 12th annual Sci-Fi Convention takes place in an auditorium that can hold up to 370 people
based on the fire code. The convention has 20 booths with 3 exhibitors working in each booth.
Which graph represents the number of Sci-Fi enthusiasts who can attend the convention at any
given time?
A.
290
300
310
320
330
340
350
360
370
380
390
400
410
20
30
40
50
60
70
80
90
100
110
120
130
140
290
300
310
320
330
340
350
360
370
380
390
400
410
290
300
310
320
330
340
350
360
370
380
390
400
410
B.
C.
D.
10. Solve the following inequalities.
A.
B.
C.
D.
11. Solve the following inequality.
A.
B.
C.
D.
12. Which of the following number lines shows the solution to the compound inequality given
below?
2x + 6 > -8 AND -3x - 2 > -14
A.
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
B.
C.
D.
Answers
1. D
2. C
3. B
4. B
5. B
6. B
7. D
8. B
9. A
10. D
11. C
12. C
Explanations
1.
-8 < 2x + 2 < 12
-10 <
2x
< 10
-5 <
x
< 5
The number line that represents this solution is shown below.
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
2. Solve the inequality to determine the correct graph.
|x + 2| + 9 > 12
|x + 2| > 3
x + 2 > 3 or x + 2 < -3
x>1
x < -5
The correct graph is shown below.
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
3. First, get the absolute value alone on one side of the inequality.
Now, eliminate the absolute value symbols by rewriting the inequality as an equivalent
compound inequality.
Now, break up the compound inequality and solve the two parts to find the correct answer.
Writing these as a single compound inequality will give the solution.
So, the correct answer is shown below.
4. On the graph, the numbers to the left of x = -3 and to the right
of x = 2 are shaded. Therefore, the compound inequality will be an "OR" inequality, or a
disjunction.
On the graph, the circles at x = -3 and x = 2 are both closed. Therefore, x < -3 OR x > 2.
5. Solve the inequality to determine the correct graph.
2|x - 1| > 6
|x - 1| > 3
x-1>3
x>4
or
x - 1 < -3
x < -2
The correct graph is shown below.
-5
-4
-3
-2
-1
0
1
2
3
4
6.
5x - 7 < -27
OR
3x - 3 > 6
5x < -20
OR
3x > 9
x < -4
OR
x > 3
5
6
7
Since the inequalities cannot be combined, the graph of the solution goes in opposite directions
as shown below.
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
7. Start by solving each of the inequalities individually.
-5x + 8 < 43
-5x < 35
x > -7
AND
AND
AND
5x - 4 < 16
5x < 20
x<4
This gives the correct answer. However, this can be rewritten in a much better form.
x > -7
-7 < x
AND
AND
x<4
x<4
Now, combine the two inequalities to get the final answer.
-7 < x < 4
8. Solve each of the inequalities individually to get the correct answer.
5x - 4 > 11
OR
-2x < -14
5x > 15
OR
x > 7
x > 3
Since x > 3 includes all the values of x such that x > 7, the correct answer is x > 3.
9. The auditorium can hold a maximum of 370 people based on the fire code. Set up an
inequality to represent the situation.
Since there are 20 booths and 3 exhibitors at each booth, there are a total of 60 exhibitors in the
auditorium. Since the maximum attendance is 370, the following inequality is true, where x
represents the number of enthusiasts.
Therefore, the following graph represents the number of Sci-Fi enthusiasts who can attend the
convention at any given time.
290
300
310
320
330
340
350
360
370
380
390
400
410
10. To solve the inequalities, isolate the x in the middle. Remember that whatever is done to the
expression in the middle must also be done to both numbers on the outside of the inequalities.
11. First, get the absolute value alone on one side of the inequality.
Now, eliminate the absolute value symbols by rewriting the inequality as an equivalent
compound inequality.
To find the solution, solve each of the inequalities.
So, the correct answer is shown below.
12.
2x + 6 > -8
AND
-3x - 2 > -14
2x > -14
AND
-3x > -12
x > -7
AND
x < 4
Graph each of the inequalities.
x > -7
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
x<4
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
Combine the graphs of the inequalities to get the final answer. The overlapping sections of the
two number lines will show the solution to the compound inequality.
-7 < x < 4
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14