# 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 ?

• A
• B
• C
• D

Q2:

What is the solution set of the equation ?

• A
• B
• C
• D

Q3:

Find the solution set of the equation .

• A
• B
• C
• D
• E

Q4:

Write the set of all solutions to the equation .

• A
• B
• C
• D
• E

Q5:

Find the solution set of .

• A
• B
• C
• D
• E

Q6:

Find algebraically the solution set of the equation .

• A
• B
• C
• D

Q7:

Liam was selling DVDs. The prices of the DVDs can be described by the equation where is the price in dollars. By graphing the equation 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
• B
• C
• D
• E

Q9:

Find algebraically the solution set of the equation .

• A
• B
• C
• D

Q10:

Find algebraically the solution set of the equation .

• A
• B
• C
• D

Q11:

Solve .

• A or
• B or
• C or
• D or
• E or

Q12:

Find algebraically in the solution set of the equation , where is constant.

• A
• B
• C
• D

Q13:

Find all possible values of given .

• A
• B or
• C or
• D or

Q14:

Given that , find the solution set of the equation .

• A
• B
• C
• D

Q15:

Given that , find the value of .

• A
• B
• C
• D

Q16:

Find algebraically the solution set of the equation .

• A
• B
• C
• D

Q17:

Write the set of all solutions to the equation .

• A
• B
• C
• D

Q18:

Find algebraically the solution set of the equation .

• A
• B
• C
• D

Q19:

Find all posssible values of given .

• A or
• B or
• C or
• D or

Q20:

Which of the following represents the interpretation for ?

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

Q21:

Find algebraically the solution set of the equation .

• A
• B
• C
• D

Q22:

Find algebraically the solution set of the equation .

• A
• B
• C
• D

Q23:

What is the solution set of the equation ?

• A
• B
• C
• D

Q24:

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

• Ayes,
• Byes,
• Cyes,
• Dno
• Eyes,

Q25:

Consider the function . Find a negative value of for which .