AnswersOC27 MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006PAbsolute Value Inequalities

Absolute Value Inequalities Answers

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1
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A student found the solution below for the given inequality.Which of the following explains whether the student is correct?

Question illustration
A
The student is completely correct because the student correctly wrote and solved the compound inequality.
B
The student is partially correct because only one part of the compound inequality is written correctly.
C
The student is partially correct because the student should have written the statements using “or” instead of “and.”
D
The student is completely incorrect because there is “ no solution “ to this inequality.
2
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What is the solution to the inequality ?

Question illustration
A
–7 < x < –1
B
1 < x < 7
C
x < –7 or x < –1
D
x > 1 or x < 7
3

A student showed the steps below while solving the inequality by graphing.Step 1:Write a system of equations: Step 2: Graph the two equations:Step 3:Identify the values of x for which :x = 3 or x = 5Step 4:Write the solution in interval notation:What is the first step in which the student made an error?

Question illustration
A
Step 1, because the student should have written a compound statement with “and”
B
Step 2, because the student should have graphed the inequalities
Option B
C
Step 3, because the values for x for which also include values between 3 and 5
Option C
D
Step 4, because the solution is one continuous interval
4

Which compound inequality is equivalent to the absolute value inequality ?

Question illustration
A
–6 > b and b > 6
B
b > –6 or b < 6
C
–6 6
D
b 6
5

Amber is solving the inequality by graphing. Which equations should Amber graph?

Question illustration
A
mc010-2.jpg
Option A
B
mc010-3.jpg
Option B
C
mc010-4.jpg
Option C
D
mc010-5.jpg
Option D
6

Which inequality is equivalent to ?

Question illustration
A
–9 > x – 4 < 9
B
–9 < x – 4 < 9
C
x – 4 < –9 or x – 4 < 9
D
x – 4 > –9 or x – 4 < 9
7

On any given day, the number of users, u, that access a certain website can be represented by the inequality . Which of the following represents the range of users that access the website each day?

Question illustration
A
or
Option A
B
mc026-4.jpg
Option B
C
or
Option C
D
mc026-7.jpg
Option D
8

Which compound inequality is equivalent to for all real numbers a, b, and c, where ?

Question illustration
A
mc006-3.jpg
Option A
B
mc006-4.jpg
Option B
C
or
Option C
D
or
Option D
9

The solution to an absolute value inequality is shown on the graph below.What is another way to show the solution?

Question illustration
A
x > –3 or x < 2
B
mc009-2.jpg
Option B
C
[–3, 2]
D
(–3, 2)
10

Which compound inequality can be used to solve the inequality ?

Question illustration
A
mc004-2.jpg
Option A
B
mc004-3.jpg
Option B
C
3x + 2 > –7 or 3x + 2 > 7
D
3x + 2 7
11

What is the solution to the inequality ?

Question illustration
A
–7 < x < –1
B
1 < x < 7
C
x < –7 or x < –1
D
x > 1 or x < 7
12

A student showed the steps below while solving the inequality by graphing.Step 1:Write a system of equations: Step 2: Graph the two equations:Step 3:Identify the values of x for which :x = 3 or x = 5Step 4:Write the solution in interval notation:What is the first step in which the student made an error?

Question illustration
A
Step 1, because the student should have written a compound statement with “and”
B
Step 2, because the student should have graphed the inequalities
Option B
C
Step 3, because the values for x for which also include values between 3 and 5
Option C
D
Step 4, because the solution is one continuous interval
13

Which compound inequality is equivalent to the absolute value inequality ?

Question illustration
A
–6 > b and b > 6
B
b > –6 or b < 6
C
–6 6
D
b 6
14

A student found the solution below for the given inequality.Which of the following explains whether the student is correct?

Question illustration
A
The student is completely correct because the student correctly wrote and solved the compound inequality.
B
The student is partially correct because only one part of the compound inequality is written correctly.
C
The student is partially correct because the student should have written the statements using “or” instead of “and.”
D
The student is completely incorrect because there is “ no solution “ to this inequality.
15

A cyclist rides at an average speed of 31 miles per hour. The cyclist’s speed, s, can differ from the average by as much as 8 miles per hour. The absolute value inequality represents this situation. If the compound inequality and also represents this situation, what is the value of x in the compound inequality?

Question illustration
A
–8
B
–8 or 8
C
8
D
8 and –8
16

On any given day, the number of users, u, that access a certain website can be represented by the inequality . Which of the following represents the range of users that access the website each day?

Question illustration
A
or
Option A
B
Option
Option B
C
or
Option C
D
Option
Option D
17

Which inequality is equivalent to ?

Question illustration
A
–9 > x – 4 < 9
B
–9 < x – 4 < 9
C
x – 4 < –9 or x – 4 < 9
D
x – 4 > –9 or x – 4 < 9
18

What is the solution, if any, to the inequality ?

Question illustration
A
all real numbers
B
no solution
C
Option
Option C
D
Option
Option D
19

Amber is solving the inequality by graphing. Which equations should Amber graph?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
20

Contessa is solving an absolute value inequality. She writes the compound inequality as her first step. Which inequality is Contessa solving?

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D

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