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Worksheet: Absolute Value Equations

Q1:

What is the solution set of the equation | ๐‘ฅ | = 9 4 ?

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

Q2:

What is the solution set of the equation | ๐‘ฅ | = 4 8 ?

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

Q3:

What is the solution set of the equation | ๐‘ฅ | = 6 5 ?

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

Q4:

What is the solution set of the equation | ๐‘ฅ | = 5 9 ?

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

  • A
  • B
  • C
  • D
  • E

Q8:

Find the solution set of the equation .

  • A
  • B
  • C
  • D

Q9:

Find the solution set of | ๐‘ฅ + 3 | = | 2 ๐‘ฅ โˆ’ 6 | .

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

Q10:

Find the solution set of | 6 ๐‘ฅ + 8 | = | โˆ’ 4 ๐‘ฅ โˆ’ 2 | .

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

Q11:

Liam was selling DVDs. The prices of the DVDs can be described by the equation | ๐‘ โˆ’ 1 5 | = 4 where ๐‘ is the price in dollars. By graphing the equation ๐‘ฆ = | ๐‘ฅ โˆ’ 1 5 | or otherwise, determine the highest and the lowest cost of a DVD.

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

Q12:

Solve | ๐‘ฅ | + 1 2 = 1 8 .

  • A ๐‘ฅ = 1 8 or ๐‘ฅ = โˆ’ 1 8
  • B ๐‘ฅ = 3 0 or ๐‘ฅ = โˆ’ 3 0
  • C ๐‘ฅ = 6 or ๐‘ฅ = โˆ’ 3 0
  • D ๐‘ฅ = 6 or ๐‘ฅ = โˆ’ 6
  • E ๐‘ฅ = 3 0 or ๐‘ฅ = โˆ’ 6

Q13:

Find algebraically the solution set of the equation .

  • A
  • B
  • C
  • D

Q14:

Find algebraically the solution set of the equation .

  • A
  • B
  • C
  • D

Q15:

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

  • A | 1 9 + ๐‘› | = 3 2 3
  • B 1 9 + | ๐‘› | = 3 2 3
  • C 1 9 โˆ’ | ๐‘› | = 3 2 3
  • D 1 9 | ๐‘› | = 3 2 3
  • E | 1 9 โˆ’ ๐‘› | = 3 2 3

Q16:

Find the solution set of the equation โˆ’ 1 0 โˆ’ โˆš 2 8 ๐‘ฅ = | โˆ’ 1 8 | in โ„ .

  • A ๏ฏ โˆ’ 4 โˆš 7 7 ๏ป
  • B ๏ซ 2 โˆš 7 ๏ท
  • C ๏ฏ 4 โˆš 7 7 ๏ป
  • D ๏ซ โˆ’ 2 โˆš 7 ๏ท

Q17:

Find algebraically the solution set of the equation 4 ๐‘ฅ | ๐‘ฅ | โˆ’ 4 ๐‘ฅ = 0 .

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

Q18:

Find algebraically the solution set of the equation | ๐‘ฅ + 3 | | ๐‘ฅ โˆ’ 3 | = 3 9 .

  • A ๏ซ โˆ’ โˆš 3 0 , โˆš 3 0 ๏ท
  • B ๏ซ 4 โˆš 3 ๏ท
  • C ๏ซ โˆš 3 0 , 4 โˆš 3 ๏ท
  • D ๏ซ โˆ’ 4 โˆš 3 , 4 โˆš 3 ๏ท

Q19:

Given that 2 ร— | โˆ’ 1 2 | = 2 ร— | ๐‘ฅ + 1 | , find the value of ๐‘ฅ .

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

Q20:

Find the solution set of 6 ๐‘ฅ + 2 2 = | โˆ’ 4 | in โ„• .

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

Q21:

Find algebraically in โ„ the solution set of the equation | ๐‘ฅ ยฑ ๐‘Ž | = โˆ’ | ๐‘ฅ ยฑ ๐‘Ž | , where ๐‘Ž is constant.

  • A { โˆ’ ๐‘Ž }
  • B { ๐‘Ž }
  • C { โˆ’ ๐‘Ž , ๐‘Ž }
  • D โˆ…

Q22:

If | โˆ’ 6 | ร— ๐‘ฅ = โˆ’ 6 6 , what is the value of ๐‘ฅ ?

Q23:

Find the solution set of โˆ’ 7 ๐‘ฅ = | โˆ’ 3 5 | in โ„• .

  • A ๏ฌ 7 5 ๏ธ
  • B { โˆ’ 5 }
  • C { โˆ’ 7 }
  • D โˆ…

Q24:

Find all possible values of ๐‘ฅ given | | | ๐‘ฅ โˆ’ 5 6 | | | = 5 6 .

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

Q25:

Given that ๐‘Ž > 0 , find the solution set of the equation | ๐‘ฅ | + ๐‘Ž = 0 .

  • A { โˆ’ ๐‘Ž , ๐‘Ž }
  • B { ๐‘Ž }
  • C { โˆ’ ๐‘Ž }
  • D โˆ…