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|=94?

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

Q2:

What is the solution set of the equation 3|𝑥|66=0?

  • A { 2 2 }
  • B { 2 2 , 2 2 }
  • C { 2 2 }
  • D { 6 6 , 6 6 }

Q3:

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

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

Q4:

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

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

Q5:

Find the solution set of |𝑥+3|=|2𝑥6|.

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

Liam was selling DVDs. The prices of the DVDs can be described by the equation |𝑐15|=4 where 𝑐 is the price in dollars. By graphing the equation 𝑦=|𝑥15| or otherwise, determine the highest and the lowest cost of a DVD.

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

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

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

Q10:

Find algebraically the solution set of the equation |𝑥+3||𝑥3|=39.

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

Q11:

Solve |𝑥|+12=18.

  • A 𝑥 = 6 or 𝑥=30
  • B 𝑥 = 3 0 or 𝑥=30
  • C 𝑥 = 1 8 or 𝑥=18
  • D 𝑥 = 3 0 or 𝑥=6
  • E 𝑥 = 6 or 𝑥=6

Q12:

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

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

Q13:

Find all possible values of 𝑥 given |||𝑥56|||=56.

  • A 5 3
  • B 5 3 or 0
  • C 5 3 or 0
  • D 3 2 or 16

Q14:

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

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

Q15:

Given that 2×|12|=2×|𝑥+1|, find the value of 𝑥.

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

Q16:

Find algebraically the solution set of the equation 11𝑥+44|𝑥+4|=𝑥.

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

Q17:

Write the set of all solutions to the equation 𝑥|𝑥|=81𝑥.

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

Q18:

Find algebraically the solution set of the equation |𝑥3||𝑥+1|=4.

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

Q19:

Find all posssible values of 𝑥 given |||𝑥+12|||=34.

  • A 5 4 or 54
  • B 1 4 or 14
  • C 1 4 or 54
  • D 5 4 or 14

Q20:

Which of the following represents the interpretation for |12𝑤|=4?

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

Q21:

Find algebraically the solution set of the equation 11𝑥17|𝑥|=196.

  • A 9 8 3
  • B { 7 }
  • C 9 8 3 , 7
  • D 7 , 9 8 3

Q22:

Find algebraically the solution set of the equation |𝑥7|=2|𝑥5|.

  • A { 5 , 7 }
  • B [ 5 , 7 ]
  • C [ 5 , 7 ]
  • D ( 5 , 7 )

Q23:

What is the solution set of the equation 6|𝑥|=7|𝑥|+20?

  • A 2 0 1 3
  • B 2 0 1 3
  • C { 1 0 , 1 0 }
  • D 2 0 1 3 , 2 0 1 3

Q24:

Matthew remembers that |𝑥|=𝑥, and uses this fact to solve the equation |𝑥|=6𝑥. Does he introduce any extraneous solutions?

  • Ayes, 𝑥=3
  • Byes, 𝑥=1
  • Cyes, 𝑥=6
  • Dno
  • Eyes, 𝑥=2

Q25:

Consider the function 𝑦=8|2𝑥+5|3. Find a negative value of 𝑥 for which 𝑦=2.

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