Worksheet: One-Variable Absolute Value Inequalities

In this worksheet, we will practice solving inequalities that contain absolute values.

Q1:

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

  • A{βˆ’13,5}
  • B(βˆ’13,5)
  • C(βˆ’5,13)
  • D(13,∞)
  • E(βˆ’βˆž,5)

Q2:

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

  • A(βˆ’2,16)
  • Bβˆ…
  • C[16,∞)
  • Dβ„βˆ’[βˆ’16,2]

Q3:

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

  • A(βˆ’9,βˆ’3)
  • B(3,∞)
  • Cβ„βˆ’[3,9]
  • D(3,9)

Q4:

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

  • Aβ„βˆ’[βˆ’13,1]
  • Bβ„βˆ’{βˆ’1,13}
  • C[1,∞)
  • D[13,∞)
  • Eβ„βˆ’(βˆ’1,13)

Q5:

Find algebraically the solution set of the inequality |8βˆ’π‘₯|>17.

  • A(βˆ’9,25)
  • Bβ„βˆ’[βˆ’9,25]
  • Cβ„βˆ’[βˆ’25,9]
  • D(βˆ’βˆž,βˆ’9)

Q6:

A factory produces cans with weight π‘₯ grams. To control the production quality, the cans are only allowed to be sold if |π‘₯βˆ’183|≀6. Determine the heaviest and the lightest weight of a can that can be sold.

  • A189 g, 183 g
  • B183 g, 6 g
  • C183 g, 177 g
  • D189 g, 177 g

Q7:

Which of the following represents the interpretation for |βˆ’3.3βˆ’π‘Ž|>5?

  • AThe distance between 5 and βˆ’3.3 is greater than π‘Ž.
  • BThe distance between βˆ’3.3 and π‘Ž is greater than 5.
  • CThe distance between βˆ’3.3 and βˆ’π‘Ž is greater than 5.
  • DThe distance between βˆ’3.3 and π‘Ž is less than 5.
  • EThe distance between βˆ’3.3 and βˆ’π‘Ž is less than 5.

Q8:

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

  • A(βˆ’βˆž,10]
  • B[4,∞)
  • C[βˆ’10,4]
  • D{βˆ’4,10}
  • E[βˆ’4,10]

Q9:

Find algebraically the solution set of the inequality |π‘₯βˆ’3|+|π‘₯βˆ’5|>6.

  • Aβ„βˆ’[1,7]
  • B(1,7)
  • C[7,∞)
  • D(βˆ’βˆž,1)

Q10:

Find the solution set of the inequality |π‘₯+5|>βˆ’7.

  • A(βˆ’12,∞)
  • Bβ„βˆ’{βˆ’12,2}
  • Cβ„βˆ’[βˆ’2,12]
  • D(βˆ’2,∞)
  • Eℝ

Q11:

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

  • Aπ‘₯>2
  • Bπ‘₯<4
  • Cπ‘₯β‰₯2
  • D2<π‘₯≀4
  • E2<π‘₯<4

Q12:

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

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

Q13:

Solve |π‘₯βˆ’6|≀5.

  • A1≀π‘₯β‰₯11
  • B1≀π‘₯≀11
  • C0≀π‘₯≀10
  • Dβˆ’1≀π‘₯β‰€βˆ’11

Q14:

Solve π‘₯βˆ’4<|2βˆ’π‘₯|.

  • Aπ‘₯<3
  • Bno solution
  • Cπ‘₯<βˆ’4
  • Dβˆ’2
  • Eany number

Q15:

Find algebraically the solution set of the inequality |8βˆ’π‘₯|+|π‘₯βˆ’8|≀6.

  • A(βˆ’βˆž,11]
  • Bβ„βˆ’(5,11)
  • C[5,11]
  • D[βˆ’11,βˆ’5]

Q16:

Find algebraically the solution set of the inequality |3βˆ’π‘₯|+|2π‘₯βˆ’6|β‰₯57.

  • Aβ„βˆ’(βˆ’22,16)
  • B[βˆ’16,22]
  • Cβ„βˆ’(βˆ’16,22)
  • D[22,∞)

Q17:

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

  • A{βˆ’7,5}
  • B(βˆ’7,5)
  • C(βˆ’5,7)
  • D(7,∞)
  • E(βˆ’βˆž,5)

Q18:

Find the solution set of the inequality |π‘₯+4|<7.

  • A{βˆ’11,3}
  • B(βˆ’11,3)
  • C(βˆ’3,11)
  • D(11,∞)
  • E(βˆ’βˆž,3)

Q19:

Use the absolute value to write an inequality statement which describes all values π‘₯ that are a distance of 8 from the number 3.

  • A|π‘₯βˆ’3|≀8
  • B|π‘₯βˆ’8|≀3
  • C|π‘₯βˆ’3|β‰₯8
  • D|π‘₯+3|≀8

Q20:

Express βˆ’4<π‘₯<4 in the form of an absolute value inequality.

  • A|π‘₯|>βˆ’4
  • B|π‘₯|<βˆ’4
  • C|π‘₯|<4
  • D|π‘₯|>4

Q21:

Express the following as an absolute value inequality: π‘₯>4, π‘₯<βˆ’4.

  • A|π‘₯|<4
  • B|π‘₯|>4
  • C|π‘₯|<βˆ’4
  • D|π‘₯|>βˆ’4

Q22:

Given that students’ marks in an exam range from 69 to 93, write an absolute value inequality to express the range of marks.

  • A|π‘₯|<12
  • B|π‘₯βˆ’81|<12
  • C|π‘₯βˆ’69|<93
  • D|π‘₯βˆ’81|<81

Q23:

An algae in the ocean can reach a maximum depth of 138 meters. Let π‘₯ represent the depth of an algae. Express, in the form of an absolute value, the range of values that π‘₯ can take.

  • A|π‘₯βˆ’69|β‰₯69
  • B|π‘₯|≀138
  • C|π‘₯|≀69
  • D|π‘₯βˆ’69|≀69

Q24:

Express 0<π‘₯<66 in the form of an absolute value inequality.

  • A|π‘₯|<33
  • B|π‘₯|<66
  • C|π‘₯βˆ’66|<66
  • D|π‘₯βˆ’33|<33

Q25:

Determine the absolute value inequality representing π‘₯βˆˆβ„βˆ’[βˆ’21,27].

  • A|π‘₯βˆ’3|>24
  • B|π‘₯|>3
  • C|π‘₯|>24
  • D|π‘₯βˆ’21|>24

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