Worksheet: Absolute Value Equations

In this worksheet, we will practice solving equations involving the absolute value.

Q1:

What is the solution set of the equation | 𝑥 | = 9 4 ?

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

Q2:

What is the solution set of the equation ?

  • A
  • B
  • C
  • D

Q3:

Find the solution set of the equation | 𝑥 + 3 | = 3 𝑥 + 7 .

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

Q4:

Write the set of all solutions to the equation | 𝑥 + 6 | = 3 .

  • A { 3 , 9 }
  • B { 3 , 3 }
  • C { 9 , 9 }
  • D { 9 , 3 }
  • E { 9 }

Q5:

Find the solution set of | 𝑥 + 3 | = | 2 𝑥 6 | .

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

Q6:

Find algebraically the solution set of the equation | 𝑥 + 4 | = 𝑥 + 4 .

  • A ] , 4 ]
  • B [ 4 , [
  • C ] , 4 ]
  • D [ 4 , [

Q7:

Amir was selling DVDs. The prices of the DVDs can be described by the equation | 𝑐 1 5 | = 4 where 𝑐 is the price in dollars. By graphing the equation 𝑦 = | 𝑥 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

Q8:

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 + | 𝑛 | = 3 2 3
  • C 1 9 | 𝑛 | = 3 2 3
  • D 1 9 | 𝑛 | = 3 2 3
  • E | 1 9 𝑛 | = 3 2 3

Q9:

Find the solution set of 7 𝑥 = | 3 5 | in .

  • A 7 5
  • B { 5 }
  • C { 7 }
  • D

Q10:

Find algebraically the solution set of the equation 4 𝑥 | 𝑥 | 4 𝑥 = 0 .

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

Q11:

Find algebraically the solution set of the equation | 𝑥 + 3 | | 𝑥 3 | = 3 9 .

  • A 3 0 , 3 0
  • B 4 3
  • C 3 0 , 4 3
  • D 4 3 , 4 3

Q12:

Solve | 𝑥 | + 1 2 = 1 8 .

  • A 𝑥 = 1 8 or 𝑥 = 1 8
  • B 𝑥 = 3 0 or 𝑥 = 3 0
  • C 𝑥 = 6 or 𝑥 = 3 0
  • D 𝑥 = 6 or 𝑥 = 6
  • E 𝑥 = 3 0 or 𝑥 = 6

Q13:

Find the solution set of the equation 1 0 2 8 𝑥 = | 1 8 | in .

  • A 4 7 7
  • B 2 7
  • C 4 7 7
  • D 2 7

Q14:

Find the solution set of 6 𝑥 + 2 2 = | 4 | in .

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

Q15:

Find algebraically in the solution set of the equation | 𝑥 ± 𝑎 | = | 𝑥 ± 𝑎 | , where 𝑎 is constant.

  • A { 𝑎 }
  • B { 𝑎 }
  • C { 𝑎 , 𝑎 }
  • D

Q16:

If | 6 | × 𝑥 = 6 6 , what is the value of 𝑥 ?

Q17:

Find all possible values of 𝑥 given | | | 𝑥 5 6 | | | = 5 6 .

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

Q18:

Given that 𝑎 > 0 , find the solution set of the equation | 𝑥 | + 𝑎 = 0 .

  • A { 𝑎 , 𝑎 }
  • B { 𝑎 }
  • C { 𝑎 }
  • D

Q19:

Given that 2 × | 1 2 | = 2 × | 𝑥 + 1 | , find the value of 𝑥 .

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

Q20:

Given that 5 × | 5 5 | = 5 × ( 𝑥 + 3 5 ) , find the value of 𝑥 .

Q21:

Find algebraically the solution set of the equation 1 1 𝑥 + 4 4 | 𝑥 + 4 | = 𝑥 .

  • A { 4 , 1 1 }
  • B { 4 , 4 }
  • C { 1 1 , 4 }
  • D { 1 1 , 1 1 }

Q22:

Write the set of all solutions to the equation 𝑥 | 𝑥 | = 8 1 𝑥 .

  • A { 9 , 9 }
  • B { 0 , 9 }
  • C { 8 1 , 8 1 }
  • D { 0 , 9 }

Q23:

Find algebraically the solution set of the equation | 𝑥 3 | | 𝑥 + 1 | = 4 .

  • A [ 1 , )
  • B { 1 }
  • C ( , 1 ]
  • D ( , 1 ]

Q24:

Find all posssible values of 𝑥 given | | | 𝑥 + 1 2 | | | = 3 4 .

  • A 1 4 or 1 4
  • B 5 4 or 1 4
  • C 5 4 or 5 4
  • D 1 4 or 5 4

Q25:

Which of the following represents the interpretation for | 1 2 𝑤 | = 4 ?

  • AThe distance between 4 and 𝑤 is 12.
  • BThe distance between 4 and 12 is 𝑤 .
  • CThe distance between 4 and 𝑤 is 12.
  • DThe distance between 12 and 𝑤 is 4.
  • EThe distance between 1 2 and 𝑤 is 4.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.