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{94,94}
  • B{94}
  • C{95,95}
  • D{94}

Q2:

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

  • A{22}
  • B{22,22}
  • C{22}
  • D{66,66}

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.

  • A19|𝑛|=323
  • B19+|𝑛|=323
  • C|19𝑛|=323
  • D|19+𝑛|=323
  • E19|𝑛|=323

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.

  • A43
  • B30,30
  • C43,43
  • D30,43

Q11:

Solve |𝑥|+12=18.

  • A𝑥=6 or 𝑥=30
  • B𝑥=30 or 𝑥=30
  • C𝑥=18 or 𝑥=18
  • D𝑥=30 or 𝑥=6
  • E𝑥=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.

  • A53
  • B53 or 0
  • C53 or 0
  • D32 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.

  • A12,12
  • B11,11
  • C11,13
  • D13,11

Q16:

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

  • A{4,4}
  • B{11,11}
  • C{11,4}
  • D{4,11}

Q17:

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

  • A{0,9}
  • B{0,9}
  • C{81,81}
  • 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.

  • A54 or 54
  • B14 or 14
  • C14 or 54
  • D54 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.

  • A983
  • B{7}
  • C983,7
  • D7,983

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?

  • A2013
  • B2013
  • C{10,10}
  • D2013,2013

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.

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