AnswersGA-GSE Algebra IIAdvanced Algebra BSolving One-Variable Equations with Systems

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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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
3

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
4

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
5

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
Option
Option B
C
[–3, 2]
D
(–3, 2)
6

What is another way to write the absolute value inequality ?

Question illustration
A
Option
Option A
B
Option
Option B
C
or
Option C
D
or
Option D
7

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
8

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

Question illustration
A
Option
Option A
B
Option
Option B
C
or
Option C
D
or
Option D
9

Which of the following represents the solution to the inequality ?

Question illustration
A
Option
Option A
B
Option
Option B
C
[–2, 7]
D
[1.5, 7.5]
10

Which compound inequality can be used to solve the inequality ?

Question illustration
A
Option
Option A
B
Option
Option B
C
3x + 2 > –7 or 3x + 2 > 7
D
3x + 2 7

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