Absolute Value Equations Practice
Get the absolute value alone, then split: |x − 1| = 9 means x − 1 = 9 or x − 1 = -9.
Last updated
Solve for x.
12 problems
- 1.
- 2.
- 3.
- 4.
- 5.
- 6.|x − 1| = 9Answerx=10, x=−8
Split the absolute value
x−1=9, x−1=−9Move −1 to the other side
x=10, x−1=−9Move −1 to the other side
x=10, x=−8
- 7.|x − 1| = 16Answerx=17, x=−15
Split the absolute value
x−1=16, x−1=−16Move −1 to the other side
x=17, x−1=−16Move −1 to the other side
x=17, x=−15
- 8.|x − 6| + 3 = 7Answerx=10, x=2
Move 3 to the other side
|x−6|=4Split the absolute value
x−6=4, x−6=−4Move −6 to the other side
x=10, x−6=−4Move −6 to the other side
x=10, x=2
- 9.7|x + 2| = 7Answerx=−1, x=−3
Move 7 to the other side
|x+2|=1Split the absolute value
x+2=1, x+2=−1Move 2 to the other side
x=−1, x+2=−1Move 2 to the other side
x=−1, x=−3
- 10.|x − 7| + 3 = 5Answerx=9, x=5
Move 3 to the other side
|x−7|=2Split the absolute value
x−7=2, x−7=−2Move −7 to the other side
x=9, x−7=−2Move −7 to the other side
x=9, x=5
- 11.7|x + 5| = 14Answerx=−3, x=−7
Move 7 to the other side
|x+5|=2Split the absolute value
x+5=2, x+5=−2Move 5 to the other side
x=−3, x+5=−2Move 5 to the other side
x=−3, x=−7
- 12.|x − 8| + 3 = 6Answerx=11, x=5
Move 3 to the other side
|x−8|=3Split the absolute value
x−8=3, x−8=−3Move −8 to the other side
x=11, x−8=−3Move −8 to the other side
x=11, x=5
If the absolute value equals a negative number, there is no solution: a distance is never negative.
Common questions
- Why are there two answers?
- Two numbers are the same distance from zero, like 6 and -6.
- When is there no solution?
- When the absolute value would have to equal a negative number.
