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Lesson: Absolute Value Inequalities

Video

14:04

Sample Question Videos

Worksheet • 23 Questions • 1 Video

Q1:

Find the solution set of the inequality | π‘₯ + 4 | < 9 .

  • A ] βˆ’ 1 3 , 5 [
  • B ] 1 3 , ∞ [
  • C ] βˆ’ ∞ , 5 [
  • D { βˆ’ 1 3 , 5 }
  • E ] βˆ’ 5 , 1 3 [

Q2:

Find algebraically the solution set of the inequality .

  • A
  • B
  • C
  • D

Q3:

Find algebraically the solution set of the inequality | 6 βˆ’ π‘₯ | < 3 .

  • A ] 3 , 9 [
  • B ℝ βˆ’ [ 3 , 9 ]
  • C ] 3 , ∞ [
  • D ] βˆ’ 9 , βˆ’ 3 [

Q4:

Find the solution set of the inequality | π‘₯ βˆ’ 6 | β‰₯ 7 .

  • A ℝ βˆ’ ] βˆ’ 1 , 1 3 [
  • B [ 1 , ∞ [
  • C [ 1 3 , ∞ [
  • D ℝ βˆ’ { βˆ’ 1 , 1 3 }
  • E ℝ βˆ’ [ βˆ’ 1 3 , 1 ]

Q5:

A body was moving with a uniform velocity of magnitude 5 cm/s from the point 𝐴 to the point 𝐢 passing through the point 𝐡 without stopping. The distance between the body and the point 𝐡 is given by 𝑑 ( 𝑑 ) = 5 | 8 βˆ’ 𝑑 | , where 𝑑 is the time in seconds, and 𝑑 is the distance in cm. Determine the distance between the body and the point 𝐡 after 5 seconds and after 11 seconds.

  • A 15 cm, 15 cm
  • B 15 cm, 5 cm
  • C 3 cm, 40 cm
  • D 5 cm, 5 cm

Q6:

A body moved from position 𝐴 to position 𝐢 passing through position 𝐡 with a uniform velocity of 3 cm/s and without stopping. If the distance between the body and position 𝐡 is given by 𝑑 ( 𝑑 ) = 3 | 7 βˆ’ 𝑑 | , where 𝑑 is the time in seconds, and 𝑑 is the distance in centimetres, determine the time interval during which the body is less than 9 cm from 𝐡 .

  • A ] 4 , 1 0 [
  • B [ 4 , 1 0 ]
  • C ] 4 , ∞ [
  • D ] 1 0 , ∞ [

Q7:

Find algebraically the solution set of the inequality | 8 βˆ’ π‘₯ | > 1 7 .

  • A ℝ βˆ’ [ βˆ’ 9 , 2 5 ]
  • B ] βˆ’ 9 , 2 5 [
  • C ] βˆ’ ∞ , βˆ’ 9 [
  • D ℝ βˆ’ [ βˆ’ 2 5 , 9 ]

Q8:

A factory produces cans with weight π‘₯ grams. To control the production quality, the cans are only allowed to be sold if | π‘₯ βˆ’ 1 8 3 | ≀ 6 . Determine the heaviest and the lightest weight of a can that can be sold.

  • A 189 g, 177 g
  • B 189 g, 183 g
  • C 183 g, 6 g
  • D 183 g, 177 g

Q9:

Which of the following represents the interpretation for | βˆ’ 3 . 3 βˆ’ π‘Ž | > 5 ?

  • AThe distance between βˆ’ 3 . 3 and π‘Ž is greater than 5.
  • BThe distance between βˆ’ 3 . 3 and π‘Ž is less than 5.
  • CThe distance between βˆ’ 3 . 3 and βˆ’ π‘Ž is greater than 5.
  • DThe distance between βˆ’ 3 . 3 and βˆ’ π‘Ž is less than 5.
  • EThe distance between 5 and βˆ’ 3 . 3 is greater than π‘Ž .

Q10:

Find the solution set of the inequality | π‘₯ βˆ’ 3 | ≀ 7 .

  • A [ βˆ’ 4 , 1 0 ]
  • B [ 4 , ∞ [
  • C ] βˆ’ ∞ , 1 0 ]
  • D { βˆ’ 4 , 1 0 }
  • E [ βˆ’ 1 0 , 4 ]

Q11:

Find algebraically the solution set of the inequality .

  • A
  • B
  • C
  • D

Q12:

Find the solution set of the inequality | π‘₯ βˆ’ 8 | > 2 .

  • A ℝ βˆ’ [ 6 , 1 0 ]
  • B ] βˆ’ 6 , ∞ [
  • C ] 1 0 , ∞ [
  • D ℝ βˆ’ { 6 , 1 0 }
  • E ℝ βˆ’ [ βˆ’ 1 0 , βˆ’ 6 ]

Q13:

Suppose that | 2 π‘₯ βˆ’ 𝑏 | < 2 and 𝑏 > 6 . Which of the following is true?

  • A π‘₯ > 2
  • B π‘₯ < 4
  • C π‘₯ β‰₯ 2
  • D 2 < π‘₯ ≀ 4
  • E 2 < π‘₯ < 4

Q14:

Suppose π‘Ž < 0 < 𝑏 . If 𝑏 > 2 , which of the following statements is true?

  • A | π‘Ž βˆ’ 𝑏 | > 2
  • B π‘Ž βˆ’ 𝑏 > βˆ’ 2
  • C | π‘Ž + 𝑏 | > 1
  • D | π‘Ž + 𝑏 | > 2
  • E | π‘Ž βˆ’ 𝑏 | < 2

Q15:

Solve | π‘₯ βˆ’ 6 | ≀ 5 .

  • A 1 ≀ π‘₯ ≀ 1 1
  • B βˆ’ 1 ≀ π‘₯ ≀ βˆ’ 1 1
  • C 0 ≀ π‘₯ ≀ 1 0
  • D 1 ≀ π‘₯ β‰₯ 1 1

Q16:

Solve π‘₯ βˆ’ 4 < | 2 βˆ’ π‘₯ | .

  • Aany number
  • B βˆ’ 2
  • C π‘₯ < βˆ’ 4
  • D no solution
  • E π‘₯ < 3

Q17:

What is the interval which represents the set of all real numbers that are less than or equal to | 6 | ?

  • A ] βˆ’ ∞ , 6 ]
  • B [ 6 , ∞ [
  • C ] 6 , ∞ [
  • D ] βˆ’ ∞ , 6 [

Q18:

Which of the following is true?

  • A ( 1 9 + ( βˆ’ 1 9 ) ) Γ— 9 < ( | 2 7 | + ( βˆ’ 2 8 ) ) Γ— | βˆ’ 9 |
  • B ( 1 9 + ( βˆ’ 1 9 ) ) Γ— 9 > ( | 2 7 | + ( βˆ’ 2 8 ) ) Γ— | βˆ’ 9 |
  • C ( 1 9 + ( βˆ’ 1 9 ) ) Γ— 9 = ( | 2 7 | + ( βˆ’ 2 8 ) ) Γ— | βˆ’ 9 |

Q19:

Find algebraically the solution set of the inequality | βˆ’ 3 βˆ’ 2 π‘₯ | + | 2 π‘₯ + 3 | < 2 6 .

  • A ] βˆ’ 8 , 5 [
  • B ℝ βˆ’ [ βˆ’ 8 , 5 ]
  • C ] βˆ’ ∞ , 5 [
  • D ] βˆ’ 5 , 8 [

Q20:

Find algebraically the solution set of the inequality | 3 βˆ’ π‘₯ | + | 2 π‘₯ βˆ’ 6 | β‰₯ 5 7 .

  • A ℝ βˆ’ ] βˆ’ 1 6 , 2 2 [
  • B [ βˆ’ 1 6 , 2 2 ]
  • C [ 2 2 , ∞ [
  • D ℝ βˆ’ ] βˆ’ 2 2 , 1 6 [

Q21:

Use the graph to find the solution set of the inequality 𝑓 ( π‘₯ ) β‰₯ 𝑔 ( π‘₯ ) .

  • A ℝ βˆ’ ] βˆ’ 4 , 2 [
  • B ℝ βˆ’ [ βˆ’ 4 , 2 ]
  • C [ βˆ’ 4 , 2 ]
  • D ] βˆ’ 4 , 2 [

Q22:

Find the solution set of the inequality | π‘₯ + 1 | < 6 .

  • A ] βˆ’ 7 , 5 [
  • B ] 7 , ∞ [
  • C ] βˆ’ ∞ , 5 [
  • D { βˆ’ 7 , 5 }
  • E ] βˆ’ 5 , 7 [

Q23:

Find the solution set of the inequality | π‘₯ βˆ’ 2 | < 4 .

  • A ] βˆ’ 2 , 6 [
  • B ] 2 , ∞ [
  • C ] βˆ’ ∞ , 6 [
  • D { βˆ’ 2 , 6 }
  • E ] βˆ’ 6 , 2 [
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