Practice
Solving Inequalities Practice
Fifty original questions covering solution steps, language, number lines, extrema, and modeling.
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Question 1
Explanation
Divide both sides by the positive number \(4\). The inequality direction stays unchanged, giving \(x<=7\).
Question 2
Explanation
Divide both sides by the positive number \(6\). The inequality direction stays unchanged, giving \(x>-3\).
Question 3
Explanation
Divide both sides by the positive number \(5\). The inequality direction stays unchanged, giving \(x<9\).
Question 4
Explanation
Divide both sides by the positive number \(8\). The inequality direction stays unchanged, giving \(x>=-2\).
Question 5
Explanation
Divide both sides by the positive number \(3\). The inequality direction stays unchanged, giving \(x>11\).
Question 6
Explanation
Undo the constant first, then divide by positive \(3\). The result is \(x<7\).
Question 7
Explanation
Undo the constant first, then divide by positive \(4\). The result is \(x>=5\).
Question 8
Explanation
Undo the constant first, then divide by positive \(6\). The result is \(x<=7\).
Question 9
Explanation
Undo the constant first, then divide by positive \(5\). The result is \(x>-3\).
Question 10
Explanation
Undo the constant first, then divide by positive \(7\). The result is \(x<-1\).
Question 11
Explanation
Dividing by negative \(-2\) reflects the order on the number line, so < reverses. The solution is \(x>-4\).
Question 12
Explanation
Dividing by negative \(-5\) reflects the order on the number line, so >= reverses. The solution is \(x<=4\).
Question 13
Explanation
Dividing by negative \(-3\) reflects the order on the number line, so <= reverses. The solution is \(x>=-5\).
Question 14
Explanation
Dividing by negative \(-4\) reflects the order on the number line, so > reverses. The solution is \(x<7\).
Question 15
Explanation
Dividing by negative \(-6\) reflects the order on the number line, so < reverses. The solution is \(x>-1.5\).
Question 16
Explanation
Collect variable terms and constants without reversing the sign. The final positive-coefficient inequality gives \(x<3\).
Question 17
Explanation
Collect variable terms and constants without reversing the sign. The final positive-coefficient inequality gives \(x>=3\).
Question 18
Explanation
Collect variable terms and constants without reversing the sign. The final positive-coefficient inequality gives \(x<=7\).
Question 19
Explanation
Collect variable terms and constants without reversing the sign. The final positive-coefficient inequality gives \(x>3\).
Question 20
Explanation
Collect variable terms and constants without reversing the sign. The final positive-coefficient inequality gives \(x<5\).
Question 21
Explanation
A download is at most 12 gigabytes. translates to \(d\le12\); the wording determines both direction and whether equality is allowed.
Question 22
Explanation
A rider must be at least 48 inches tall. translates to \(h\ge48\); the wording determines both direction and whether equality is allowed.
Question 23
Explanation
The temperature does not exceed 30 degrees. translates to \(t\le30\); the wording determines both direction and whether equality is allowed.
Question 24
Explanation
The account has no less than 75 dollars. translates to \(a\ge75\); the wording determines both direction and whether equality is allowed.
Question 25
Explanation
The wait is fewer than 20 minutes. translates to \(w<20\); the wording determines both direction and whether equality is allowed.
Question 26
Explanation
The endpoint and ray show \(x<3\): the open circle excludes \(3\).
Question 27
Explanation
The endpoint and ray show \(x>-2\): the open circle excludes \(-2\).
Question 28
Explanation
The endpoint and ray show \(x<=5\): the closed circle includes \(5\).
Question 29
Explanation
The endpoint and ray show \(x>=-4\): the closed circle includes \(-4\).
Question 30
Explanation
The endpoint and ray show \(x<-1\): the open circle excludes \(-1\).
Question 31
Explanation
Integers are discrete. The greatest integer allowed by \(n<11\) is \(10\).
Question 32
Explanation
Integers are discrete. The greatest integer allowed by \(n\le-2\) is \(-2\).
Question 33
Explanation
Integers are discrete. The greatest integer allowed by \(n<0\) is \(-1\).
Question 34
Explanation
Integers are discrete. The greatest integer allowed by \(n\le18\) is \(18\).
Question 35
Explanation
Integers are discrete. The greatest integer allowed by \(n<105\) is \(104\).
Question 36
Explanation
Clear the decimal or fractional coefficient carefully and preserve or reverse direction according to its sign. The result is \(x>6\).
Question 37
Explanation
Clear the decimal or fractional coefficient carefully and preserve or reverse direction according to its sign. The result is \(x\le12\).
Question 38
Explanation
Clear the decimal or fractional coefficient carefully and preserve or reverse direction according to its sign. The result is \(x>-5\).
Question 39
Explanation
Clear the decimal or fractional coefficient carefully and preserve or reverse direction according to its sign. The result is \(x\le-15\).
Question 40
Explanation
Clear the decimal or fractional coefficient carefully and preserve or reverse direction according to its sign. The result is \(x\ge4\).
Question 41
Explanation
The graph represents \(x>=2\). Substituting \(5\) makes that statement true.
Question 42
Explanation
The graph represents \(x<-1\). Substituting \(0\) makes that statement false.
Question 43
Explanation
The graph represents \(x<=4\). Substituting \(4\) makes that statement true.
Question 44
Explanation
The graph represents \(x>3\). Substituting \(3\) makes that statement false.
Question 45
Explanation
The graph represents \(x<6\). Substituting \(-2\) makes that statement true.
Question 46
Explanation
Translate the limiting phrase, solve the resulting inequality, and retain the contextual direction. This gives \(18+7h\le67\) and \(h\le7\).
Question 47
Explanation
Translate the limiting phrase, solve the resulting inequality, and retain the contextual direction. This gives \(12+3m\ge30\) and \(m\ge6\).
Question 48
Explanation
Translate the limiting phrase, solve the resulting inequality, and retain the contextual direction. This gives \(165+15r>240\) and \(r>5\).
Question 49
Explanation
Translate the limiting phrase, solve the resulting inequality, and retain the contextual direction. This gives \(8c\le96\) and \(c\le12\).
Question 50
Explanation
Translate the limiting phrase, solve the resulting inequality, and retain the contextual direction. This gives \(44+6w\ge80\) and \(w\ge6\).
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Questions to review
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- Question 1One-step inequalitiesEasy
- Question 2One-step inequalitiesEasy
- Question 3One-step inequalitiesEasy
- Question 4One-step inequalitiesEasy
- Question 5One-step inequalitiesEasy
- Question 6Two-step inequalitiesEasy
- Question 7Two-step inequalitiesEasy
- Question 8Two-step inequalitiesEasy
- Question 9Two-step inequalitiesEasy
- Question 10Two-step inequalitiesEasy
- Question 11Negative-coefficient inequalitiesEasy
- Question 12Negative-coefficient inequalitiesEasy
- Question 13Negative-coefficient inequalitiesEasy
- Question 14Negative-coefficient inequalitiesEasy
- Question 15Negative-coefficient inequalitiesEasy
- Question 16Variables on both sidesMedium
- Question 17Variables on both sidesMedium
- Question 18Variables on both sidesMedium
- Question 19Variables on both sidesMedium
- Question 20Variables on both sidesMedium
- Question 21Inequality languageMedium
- Question 22Inequality languageMedium
- Question 23Inequality languageMedium
- Question 24Inequality languageMedium
- Question 25Inequality languageMedium
- Question 26Number-line interpretationMedium
- Question 27Number-line interpretationMedium
- Question 28Number-line interpretationMedium
- Question 29Number-line interpretationMedium
- Question 30Number-line interpretationMedium
- Question 31Greatest integer valuesMedium
- Question 32Greatest integer valuesMedium
- Question 33Greatest integer valuesMedium
- Question 34Greatest integer valuesMedium
- Question 35Greatest integer valuesMedium
- Question 36Fraction and decimal inequalitiesMedium
- Question 37Fraction and decimal inequalitiesMedium
- Question 38Fraction and decimal inequalitiesMedium
- Question 39Fraction and decimal inequalitiesMedium
- Question 40Fraction and decimal inequalitiesMedium
- Question 41Testing possible valuesHard
- Question 42Testing possible valuesHard
- Question 43Testing possible valuesHard
- Question 44Testing possible valuesHard
- Question 45Testing possible valuesHard
- Question 46Contextual inequality modelingHard
- Question 47Contextual inequality modelingHard
- Question 48Contextual inequality modelingHard
- Question 49Contextual inequality modelingHard
- Question 50Contextual inequality modelingHard