Practice
Compound and Absolute Value Inequalities Practice
Fifty original questions covering AND, OR, distance patterns, edge cases, integers, and graphs.
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Question 1
Explanation
Apply each operation to all three parts. The common interval is \(-3<x\le4\).
Question 2
Explanation
Apply each operation to all three parts. The common interval is \(2\le x<6\).
Question 3
Explanation
Apply each operation to all three parts. The common interval is \(-2<x\le4\).
Question 4
Explanation
Apply each operation to all three parts. The common interval is \(-5<x\le1\).
Question 5
Explanation
Apply each operation to all three parts. The common interval is \(-3\le x\le3\).
Question 6
Explanation
Solve each branch independently and preserve OR. The result is \(x<-4\text{ or }x\ge4\).
Question 7
Explanation
Solve each branch independently and preserve OR. The result is \(x>5\text{ or }x\le-3\).
Question 8
Explanation
Solve each branch independently and preserve OR. The result is \(x>4\text{ or }x>5\).
Question 9
Explanation
Solve each branch independently and preserve OR. The result is \(x\le-4\text{ or }x>9\).
Question 10
Explanation
Solve each branch independently and preserve OR. The result is \(x<-1\text{ or }x\ge6\).
Question 11
Explanation
The absolute value sets an inside-distance condition. Write a three-part inequality and solve to obtain \(-3<x<7\).
Question 12
Explanation
The absolute value sets an inside-distance condition. Write a three-part inequality and solve to obtain \(-4\le x\le3\).
Question 13
Explanation
The absolute value sets an inside-distance condition. Write a three-part inequality and solve to obtain \(-1<x<5\).
Question 14
Explanation
The absolute value sets an inside-distance condition. Write a three-part inequality and solve to obtain \(-6\le x\le-2\).
Question 15
Explanation
The absolute value sets an inside-distance condition. Write a three-part inequality and solve to obtain \(-3<x<3\).
Question 16
Explanation
The distance must be large enough to lie outside both boundaries, giving \(x<-5\text{ or }x>3\).
Question 17
Explanation
The distance must be large enough to lie outside both boundaries, giving \(x\le-1\text{ or }x\ge4\).
Question 18
Explanation
The distance must be large enough to lie outside both boundaries, giving \(x<-6\text{ or }x>2\).
Question 19
Explanation
The distance must be large enough to lie outside both boundaries, giving \(x\le4\text{ or }x\ge10\).
Question 20
Explanation
The distance must be large enough to lie outside both boundaries, giving \(x<-4\text{ or }x>4\).
Question 21
Explanation
Absolute value is never negative. Comparing the nonnegative left side with the target gives no real solution.
Question 22
Explanation
Absolute value is never negative. Comparing the nonnegative left side with the target gives all real numbers.
Question 23
Explanation
Absolute value is never negative. Comparing the nonnegative left side with the target gives x=-5/2.
Question 24
Explanation
Absolute value is never negative. Comparing the nonnegative left side with the target gives all real numbers.
Question 25
Explanation
Absolute value is never negative. Comparing the nonnegative left side with the target gives no real solution.
Question 26
Explanation
The shaded segment is the intersection between the endpoints. Its endpoint markers give \(-2<x\le4\).
Question 27
Explanation
The shaded segment is the intersection between the endpoints. Its endpoint markers give \(-5\lex<1\).
Question 28
Explanation
The shaded segment is the intersection between the endpoints. Its endpoint markers give \(0\lex\le5\).
Question 29
Explanation
The shaded segment is the intersection between the endpoints. Its endpoint markers give \(-4<x<-1\).
Question 30
Explanation
The shaded segment is the intersection between the endpoints. Its endpoint markers give \(2<x\le6\).
Question 31
Explanation
The graph shows values no farther than \(2\) units from zero, so it represents \(|x|\le2\).
Question 32
Explanation
The graph shows values farther than \(3\) units from zero, so it represents \(|x|>3\).
Question 33
Explanation
The graph shows values no farther than \(4\) units from zero, so it represents \(|x|\le4\).
Question 34
Explanation
The graph shows values farther than \(5\) units from zero, so it represents \(|x|>5\).
Question 35
Explanation
The graph shows values no farther than \(6\) units from zero, so it represents \(|x|\le6\).
Question 36
Explanation
List the integers in the displayed interval and count each included endpoint correctly. There are \(7\).
Question 37
Explanation
List the integers in the displayed interval and count each included endpoint correctly. There are \(7\).
Question 38
Explanation
List the integers in the displayed interval and count each included endpoint correctly. There are \(6\).
Question 39
Explanation
List the integers in the displayed interval and count each included endpoint correctly. There are \(6\).
Question 40
Explanation
List the integers in the displayed interval and count each included endpoint correctly. There are \(7\).
Question 41
Explanation
The words identify interval direction, connector, and endpoint inclusion. The correct model is \(70\le s<90\).
Question 42
Explanation
The words identify interval direction, connector, and endpoint inclusion. The correct model is \(x<-4\text{ or }x\ge6\).
Question 43
Explanation
The words identify interval direction, connector, and endpoint inclusion. The correct model is \(|t-20|\le3\).
Question 44
Explanation
The words identify interval direction, connector, and endpoint inclusion. The correct model is \(|m-12|>5\).
Question 45
Explanation
The words identify interval direction, connector, and endpoint inclusion. The correct model is \(8<t\le15\).
Question 46
Explanation
First isolate the absolute value, inspect the positive target, and then use the correct inside or outside form. The result is \(-2<x<7\).
Question 47
Explanation
First isolate the absolute value, inspect the positive target, and then use the correct inside or outside form. The result is \(x\le-8\text{ or }x\ge4\).
Question 48
Explanation
First isolate the absolute value, inspect the positive target, and then use the correct inside or outside form. The result is \(-5/3\le x\le7/3\).
Question 49
Explanation
First isolate the absolute value, inspect the positive target, and then use the correct inside or outside form. The result is \(x<-1\text{ or }x>5\).
Question 50
Explanation
First isolate the absolute value, inspect the positive target, and then use the correct inside or outside form. The result is \(-1<x<7\).
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Questions to review
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- Question 1AND compound inequalitiesEasy
- Question 2AND compound inequalitiesEasy
- Question 3AND compound inequalitiesEasy
- Question 4AND compound inequalitiesEasy
- Question 5AND compound inequalitiesEasy
- Question 6OR compound inequalitiesEasy
- Question 7OR compound inequalitiesEasy
- Question 8OR compound inequalitiesEasy
- Question 9OR compound inequalitiesEasy
- Question 10OR compound inequalitiesEasy
- Question 11Absolute-value inside inequalitiesEasy
- Question 12Absolute-value inside inequalitiesEasy
- Question 13Absolute-value inside inequalitiesEasy
- Question 14Absolute-value inside inequalitiesEasy
- Question 15Absolute-value inside inequalitiesEasy
- Question 16Absolute-value outside inequalitiesMedium
- Question 17Absolute-value outside inequalitiesMedium
- Question 18Absolute-value outside inequalitiesMedium
- Question 19Absolute-value outside inequalitiesMedium
- Question 20Absolute-value outside inequalitiesMedium
- Question 21Absolute-value edge casesMedium
- Question 22Absolute-value edge casesMedium
- Question 23Absolute-value edge casesMedium
- Question 24Absolute-value edge casesMedium
- Question 25Absolute-value edge casesMedium
- Question 26Compound number-line graphsMedium
- Question 27Compound number-line graphsMedium
- Question 28Compound number-line graphsMedium
- Question 29Compound number-line graphsMedium
- Question 30Compound number-line graphsMedium
- Question 31Absolute-value number-line graphsMedium
- Question 32Absolute-value number-line graphsMedium
- Question 33Absolute-value number-line graphsMedium
- Question 34Absolute-value number-line graphsMedium
- Question 35Absolute-value number-line graphsMedium
- Question 36Integer solutions of compoundsMedium
- Question 37Integer solutions of compoundsMedium
- Question 38Integer solutions of compoundsMedium
- Question 39Integer solutions of compoundsMedium
- Question 40Integer solutions of compoundsMedium
- Question 41Compound inequality translationHard
- Question 42Compound inequality translationHard
- Question 43Compound inequality translationHard
- Question 44Compound inequality translationHard
- Question 45Compound inequality translationHard
- Question 46Multi-step absolute-value inequalitiesHard
- Question 47Multi-step absolute-value inequalitiesHard
- Question 48Multi-step absolute-value inequalitiesHard
- Question 49Multi-step absolute-value inequalitiesHard
- Question 50Multi-step absolute-value inequalitiesHard