Linear Inequalities practice questions

Linear Inequalities questions

Pick an answer before you look. Tapping a choice shows which one was right and opens the worked explanation, and a miss is remembered so Weak Skills can replay that skill. It stays in this browser.

1. 1Linear inequalitiesFoundation

   Which inequality is equivalent to 2x - 7 > 5?Which inequality is equivalent to 2x - 7 > 5?

   • Ax < 1x < 1
   • Bx < 6x < 6
   • Cx > 1x > 1
   • Dx > 6x > 6
   Show the answer and explanationHide the explanation

   Answer: x > 6x > 6

   Add 7 to both sides to get 2x > 12. Divide by positive 2, so x > 6.Add 7 to both sides to get 2x > 12. Divide by positive 2, so x > 6.

   How did you do?Got itMissed it
2. 2Linear inequalitiesStandard

   A delivery van can carry at most 900 kilograms. It is already loaded with 240 kilograms. If each crate weighs 30 kilograms, what is the greatest number of crates it can still take?A delivery van can carry at most 900 kilograms. It is already loaded with 240 kilograms. If each crate weighs 30 kilograms, what is the greatest number of crates it can still take?

   • A3030
   • B2323
   • C2020
   • D2222
   Show the answer and explanationHide the explanation

   Answer: 2222

   The remaining capacity is 900 - 240 = 660 kilograms. Dividing by 30 gives 22 crates exactly, and 23 crates would exceed the limit.The remaining capacity is 900 - 240 = 660 kilograms. Dividing by 30 gives 22 crates exactly, and 23 crates would exceed the limit.

   How did you do?Got itMissed it
3. 3Linear inequalitiesStandard

   A taxi charges a $3 flag fee plus $1.80 per mile. What is the greatest whole number of miles that can be traveled for $30?A taxi charges a $3 flag fee plus $1.80 per mile. What is the greatest whole number of miles that can be traveled for $30?

   • A1515
   • B1717
   • C1414
   • D1616
   Show the answer and explanationHide the explanation

   Answer: 1515

   Solve 3 + 1.80m ≤ 30, so 1.80m ≤ 27 and m ≤ 15. Exactly 15 miles costs $30, and 16 would exceed it.Solve 3 + 1.80m ≤ 30, so 1.80m ≤ 27 and m ≤ 15. Exactly 15 miles costs $30, and 16 would exceed it.

   How did you do?Got itMissed it
4. 4Linear inequalitiesStandard

   A van can carry at most 1,200 kg. It already holds 340 kg of equipment, and each box loaded weighs 24 kg. What is the greatest number of boxes it can take?A van can carry at most 1,200 kg. It already holds 340 kg of equipment, and each box loaded weighs 24 kg. What is the greatest number of boxes it can take?

   • A3636
   • B3535
   • C5050
   • D6464
   Show the answer and explanationHide the explanation

   Answer: 3535

   The condition is 340 + 24b ≤ 1200, so 24b ≤ 860 and b ≤ 35.83. Because b counts boxes it must be a whole number, and rounding up to 36 puts the load at 1,204 kg, over the limit.The condition is 340 + 24b ≤ 1200, so 24b ≤ 860 and b ≤ 35.83. Because b counts boxes it must be a whole number, and rounding up to 36 puts the load at 1,204 kg, over the limit.

   How did you do?Got itMissed it
5. 5Linear inequalitiesStandard

   Enter the greatest integer value of x for which 5x - 8 < 27.Enter the greatest integer value of x for which 5x - 8 < 27.

   Student-produced response: write your own answer rather than choosing one.

   Show the answer and explanationHide the explanation

   Answer: 66

   Adding 8 gives 5x < 35, so x < 7. The inequality is strict, so 7 itself does not satisfy it and the greatest integer that does is 6.Adding 8 gives 5x < 35, so x < 7. The inequality is strict, so 7 itself does not satisfy it and the greatest integer that does is 6.

   How did you do?Got itMissed it
6. 6Linear inequalitiesStandard

   Which describes every solution to 4 - 2x < 10?Which describes every solution to 4 - 2x < 10?

   • Ax > -3x > -3
   • Bx < -3x < -3
   • Cx < 3x < 3
   • Dx > 3x > 3
   Show the answer and explanationHide the explanation

   Answer: x > -3x > -3

   Subtracting 4 gives -2x < 6. Dividing by -2 reverses the inequality, so x > -3. Test x = -2: 4 + 4 = 8, which is less than 10. Failing to flip the sign gives x < -3, which fails that test.Subtracting 4 gives -2x < 6. Dividing by -2 reverses the inequality, so x > -3. Test x = -2: 4 + 4 = 8, which is less than 10. Failing to flip the sign gives x < -3, which fails that test.

   How did you do?Got itMissed it
7. 7Linear inequalitiesChallenge

   Which inequality is equivalent to -3x + 4 ≤ 19?Which inequality is equivalent to -3x + 4 ≤ 19?

   • Ax ≥ -5x ≥ -5
   • Bx ≤ 5x ≤ 5
   • Cx ≤ -5x ≤ -5
   • Dx ≥ 5x ≥ 5
   Show the answer and explanationHide the explanation

   Answer: x ≥ -5x ≥ -5

   Subtract 4 to get -3x ≤ 15. Dividing by a negative number reverses the inequality, so x ≥ -5.Subtract 4 to get -3x ≤ 15. Dividing by a negative number reverses the inequality, so x ≥ -5.

   How did you do?Got itMissed it
8. 8Linear inequalitiesChallenge

   Which values of x satisfy both 2x + 1 > 7 and 5 - x > 0?Which values of x satisfy both 2x + 1 > 7 and 5 - x > 0?

   • AThere are no such values.There are no such values.
   • B3 < x < 53 < x < 5
   • Cx < 5x < 5
   • Dx > 3x > 3
   Show the answer and explanationHide the explanation

   Answer: 3 < x < 53 < x < 5

   The first gives 2x > 6, so x > 3. The second gives x < 5. Both hold only between them, which is 3 < x < 5.The first gives 2x > 6, so x > 3. The second gives x < 5. Both hold only between them, which is 3 < x < 5.

   How did you do?Got itMissed it
9. 9Linear inequalitiesChallenge

   For how many integers x is -2 < 3x - 5 ≤ 7?For how many integers x is -2 < 3x - 5 ≤ 7?

   • A33
   • B55
   • C44
   • D22
   Show the answer and explanationHide the explanation

   Answer: 33

   Add 5 throughout: 3 < 3x ≤ 12. Divide by 3: 1 < x ≤ 4. The integers are 2, 3 and 4, so there are three.Add 5 throughout: 3 < 3x ≤ 12. Divide by 3: 1 < x ≤ 4. The integers are 2, 3 and 4, so there are three.

   How did you do?Got itMissed it
10. 10Linear inequalitiesChallenge

    Which describes every solution to -3x + 7 ≥ 22?Which describes every solution to -3x + 7 ≥ 22?

    • Ax ≥ -5x ≥ -5
    • Bx ≥ 5x ≥ 5
    • Cx ≤ 5x ≤ 5
    • Dx ≤ -5x ≤ -5
    Show the answer and explanationHide the explanation

    Answer: x ≤ -5x ≤ -5

    Subtracting 7 gives -3x ≥ 15. Dividing by a negative reverses the inequality, so x ≤ -5. Test x = -6: -3(-6) + 7 = 25, which is at least 22. Forgetting to flip the sign is what this question is built around.Subtracting 7 gives -3x ≥ 15. Dividing by a negative reverses the inequality, so x ≤ -5. Test x = -6: -3(-6) + 7 = 25, which is at least 22. Forgetting to flip the sign is what this question is built around.

    How did you do?Got itMissed it