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Lesson: Absolute Value Equations

In this lesson, we will learn how to solve equations involving the absolute value.

Video

13:10

Sample Question Videos

00:54
02:16
02:58

Worksheet • 25 Questions • 4 Videos

Q1:

What is the solution set of the equation | π‘₯ | = 9 4 ?

  • A { βˆ’ 9 4 , 9 4 }
  • B { 9 4 }
  • C { βˆ’ 9 5 , 9 5 }
  • D { βˆ’ 9 4 }

Q2:

What is the solution set of the equation | π‘₯ | = 4 8 ?

  • A { βˆ’ 4 8 , 4 8 }
  • B { 4 8 }
  • C { βˆ’ 4 9 , 4 9 }
  • D { βˆ’ 4 8 }

Q3:

What is the solution set of the equation | π‘₯ | = 6 5 ?

  • A { βˆ’ 6 5 , 6 5 }
  • B { 6 5 }
  • C { βˆ’ 6 6 , 6 6 }
  • D { βˆ’ 6 5 }

Q4:

What is the solution set of the equation | π‘₯ | = 5 9 ?

  • A { βˆ’ 5 9 , 5 9 }
  • B { 5 9 }
  • C { βˆ’ 6 0 , 6 0 }
  • D { βˆ’ 5 9 }

Q5:

What is the solution set of the equation ?

  • A
  • B
  • C
  • D

Q6:

What is the solution set of the equation ?

  • A
  • B
  • C
  • D

Q7:

Find the solution set of the equation | π‘₯ + 3 | = βˆ’ 3 π‘₯ + 7 .

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

Q8:

Find the solution set of the equation | π‘₯ + 8 | = βˆ’ 8 π‘₯ βˆ’ 1 .

  • A { βˆ’ 1 }
  • B { βˆ’ 1 , 1 }
  • C { 1 }
  • D [ βˆ’ 1 , 1 ]

Q9:

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

  • A { 9 , 1 }
  • B { βˆ’ 9 }
  • C { 9 }
  • D { βˆ’ 1 }
  • E { 1 }

Q10:

Find the solution set of | 6 π‘₯ + 8 | = | βˆ’ 4 π‘₯ βˆ’ 2 | .

  • A { βˆ’ 1 , βˆ’ 3 }
  • B { 1 }
  • C { βˆ’ 1 }
  • D { 3 }
  • E { βˆ’ 3 }

Q11:

Amir was selling DVDs. The prices of the DVDs can be described by the equation | 𝑐 βˆ’ 1 5 | = 4 where 𝑐 is the price in dollars. By graphing the equation 𝑦 = | π‘₯ βˆ’ 1 5 | or otherwise, determine the highest and the lowest cost of a DVD.

  • Ahighest cost: $19, lowest cost: $11
  • Bhighest cost: $19, lowest cost: $7
  • Chighest cost: $19, lowest cost: $15
  • Dhighest cost: $11, lowest cost: $7
  • Ehighest cost: $15, lowest cost: $11

Q12:

Solve | π‘₯ | + 1 2 = 1 8 .

  • A π‘₯ = 6 or π‘₯ = βˆ’ 6
  • B π‘₯ = 3 0 or π‘₯ = βˆ’ 6
  • C π‘₯ = 3 0 or π‘₯ = βˆ’ 3 0
  • D π‘₯ = 6 or π‘₯ = βˆ’ 3 0
  • E π‘₯ = 1 8 or π‘₯ = βˆ’ 1 8

Q13:

Find algebraically the solution set of the equation | π‘₯ + 4 | = π‘₯ + 4 .

  • A [ βˆ’ 4 , ∞ [
  • B [ 4 , ∞ [
  • C ] βˆ’ ∞ , 4 ]
  • D ] βˆ’ ∞ , βˆ’ 4 ]

Q14:

Find algebraically the solution set of the equation | π‘₯ + 1 0 | = π‘₯ + 1 0 .

  • A [ βˆ’ 1 0 , ∞ [
  • B [ 1 0 , ∞ [
  • C ] βˆ’ ∞ , 1 0 ]
  • D ] βˆ’ ∞ , βˆ’ 1 0 ]

Q15:

Write an equation that represents the following: 19 times the absolute value of a number is equal to 323.

  • A 1 9 | 𝑛 | = 3 2 3
  • B | 1 9 βˆ’ 𝑛 | = 3 2 3
  • C 1 9 + | 𝑛 | = 3 2 3
  • D 1 9 βˆ’ | 𝑛 | = 3 2 3
  • E | 1 9 + 𝑛 | = 3 2 3

Q16:

Find the solution set of the equation βˆ’ 1 0 βˆ’ √ 2 8 π‘₯ = | βˆ’ 1 8 | in ℝ .

  • A  βˆ’ 2 √ 7 
  • B  2 √ 7 
  • C  4 √ 7 7 
  • D  βˆ’ 4 √ 7 7 

Q17:

Find algebraically the solution set of the equation 4 π‘₯ | π‘₯ | βˆ’ 4 π‘₯ = 0 .

  • A { βˆ’ 1 , 0 , 1 }
  • B { 0 , 1 }
  • C { βˆ’ 4 , 0 , 4 }
  • D { βˆ’ 1 , 1 }

Q18:

Find algebraically the solution set of the equation | π‘₯ + 3 | | π‘₯ βˆ’ 3 | = 3 9 .

  • A  βˆ’ 4 √ 3 , 4 √ 3 
  • B  4 √ 3 
  • C  √ 3 0 , 4 √ 3 
  • D  βˆ’ √ 3 0 , √ 3 0 

Q19:

Given that 2 Γ— | βˆ’ 1 2 | = 2 Γ— | π‘₯ + 1 | , find the value of π‘₯ .

  • A 1 1 , βˆ’ 1 3
  • B 1 3 , βˆ’ 1 1
  • C 1 1 , βˆ’ 1 1
  • D 1 2 , βˆ’ 1 2

Q20:

Find the solution set of 6 π‘₯ + 2 2 = | βˆ’ 4 | in β„• .

  • A βˆ…
  • B { βˆ’ 2 6 }
  • C { 1 8 }
  • D { 2 6 }
  • E { βˆ’ 4 }

Q21:

Find algebraically in ℝ the solution set of the equation | π‘₯ Β± π‘Ž | = βˆ’ | π‘₯ Β± π‘Ž | , where π‘Ž is constant.

  • A βˆ…
  • B { π‘Ž }
  • C { βˆ’ π‘Ž , π‘Ž }
  • D { βˆ’ π‘Ž }

Q22:

If | βˆ’ 6 | Γ— π‘₯ = βˆ’ 6 6 , what is the value of π‘₯ ?

Q23:

Find the solution set of βˆ’ 7 π‘₯ = | βˆ’ 3 5 | in β„• .

  • A βˆ…
  • B { βˆ’ 5 }
  • C { βˆ’ 7 }
  • D  7 5 

Q24:

Find all possible values of π‘₯ given | | | π‘₯ βˆ’ 5 6 | | | = 5 6 .

  • A 5 3 or 0
  • B βˆ’ 5 3 or 0
  • C 3 2 or βˆ’ 1 6
  • D βˆ’ 5 3

Q25:

Given that π‘Ž > 0 , find the solution set of the equation | π‘₯ | + π‘Ž = 0 .

  • A βˆ…
  • B { π‘Ž }
  • C { βˆ’ π‘Ž }
  • D { βˆ’ π‘Ž , π‘Ž }
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