MATH 31
U1A LESSON #4
SOLVING ABSOLUTE VALUE EQUATIONS
NAME ANSWERS
(𝟕, 𝟗)
(−𝟐, 𝟗)
Practice
1. |2𝑥 − 5| = 9
𝟐𝒙 − 𝟓 = 𝟗
x=7
−(𝟐𝒙 − 𝟓) = 𝟗
−𝟐𝒙 + 𝟓 = 𝟗
−𝟐𝒙 = 𝟒
x= –2
2. |1 − 3𝑥| = 7
𝟏 − 𝟑𝒙 = 𝟕
x= –2
−(𝟏 − 𝟑𝒙) = 𝟕
−𝟏 + 𝟑𝒙 = 𝟕
𝟑𝒙 = 𝟖
𝟖
x= 𝟑
(−𝟐, 𝟕)
𝟖
( , 𝟕)
𝟑
3. |4𝑥 − 1| + 5 = 8
|𝟒𝒙 − 𝟏| = 𝟑
𝟒𝒙 − 𝟏 = 𝟑
𝟒𝒙 = 𝟒
x= 1
−(𝟒𝒙 − 𝟏) = 𝟑
−𝟒𝒙 + 𝟏 = 𝟑
−𝟒𝒙 = 𝟐
𝟏
x = −𝟐
U1A L4 ANS Abs Value Equations
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𝟏
(− , 𝟖)
𝟐
(𝟏, 𝟖)
MATH 31
U1A LESSON #4
SOLVING ABSOLUTE VALUE EQUATIONS
NAME ANSWERS
4. 1 − |𝑥 + 3| = −2
𝟑=𝒙+𝟑
𝒙=𝟎
(𝟎, −𝟐)
(−𝟔, −𝟐)
𝟑 = |𝒙 + 𝟑|
𝟑 = −(𝒙 + 𝟑)
𝟑 = −𝒙 − 𝟑
𝒙 = −𝟔
5. |2𝑥 − 4| = 0
𝟐𝒙 − 𝟒 = 𝟎
𝟐𝒙 = 𝟒
x= 2
(𝟐, 𝟎)
6. |3𝑥 − 2| + 5 = 3
|𝟑𝒙 − 𝟐| = −𝟐
No Solution
U1A L4 ANS Abs Value Equations
Page 2 of 4
MATH 31
U1A LESSON #4
SOLVING ABSOLUTE VALUE EQUATIONS
NAME ANSWERS
Practice
7. |3𝑥 + 5| = 2𝑥
𝟑𝒙 + 𝟓 = 𝟐𝒙
𝒙 = −𝟓
−(𝟑𝒙 + 𝟓) = 𝟐𝒙
𝒙 = −𝟏
CHECK
|3(−𝟓) + 5| = 2(−𝟓)
10 ≠ −10
CHECK
|3(−𝟏) + 5| = 2(−𝟏)
2 ≠ −2
There is NO solution
8. |1 − 𝑥| = 3𝑥 − 2
𝟏 − 𝒙 = 𝟑𝒙 − 𝟐
−𝟒𝒙 = −𝟑
𝟑
𝒙=
𝟒
CHECK
𝟑
𝟑
|1 − | = 3 ( ) − 2
𝟒
𝟒
1 1
=
4 4
𝟏 − 𝒙 = −(𝟑𝒙 − 𝟐) = −𝟑𝒙 + 𝟐
𝟐𝒙 = 𝟏
𝟏
𝒙=
𝟐
CHECK
𝟏
𝟏
|1 − | = 3 ( ) − 2
𝟐
𝟐
1
1
≠−
2
2
𝟑 1
( , )
𝟒 4
1
9. |𝑥 − 2| = − 2 𝑥 + 3
𝟏
𝒙−𝟐=− 𝒙+𝟑
𝟐
𝟑
𝒙=𝟓
𝟐
𝟐 𝟏𝟎
𝒙 = 𝟓× =
𝟑
𝟑
CHECK
𝟏𝟎
1 𝟏𝟎
| − 2| = − ( ) + 3
𝟑
2 𝟑
4
10 18
=− +
3
6
6
4 4
=
3 3
U1A L4 ANS Abs Value Equations
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𝟏
𝟏
𝒙 − 𝟐 = − (− 𝒙 + 𝟑) = 𝒙 − 𝟑
𝟐
𝟐
𝟏
𝒙 = −𝟏
𝟐
𝟐
𝒙 = −𝟏× = −𝟐
𝟏
CHECK
(−𝟐, 4)
1
|−𝟐 − 2| = − (−𝟐) + 3
2
4=4
𝟏𝟎 4
( , )
𝟑 3
MATH 31
U1A LESSON #4
SOLVING ABSOLUTE VALUE EQUATIONS
NAME ANSWERS
10. |𝑥 + 6| = |2𝑥|
(𝟔, 12)
𝒙 + 𝟔 = 𝟐𝒙
𝟔=𝒙
𝒙 + 𝟔 = −𝟐𝒙
𝟑𝒙 = −𝟔
𝒙 = −𝟐
(−𝟐, 4)
11. |1 − 3𝑥| = |𝑥 − 7|
𝟏 − 𝟑𝒙 = 𝒙 − 𝟕
−𝟒𝒙 = −𝟖
𝒙=𝟐
𝟏 − 𝟑𝒙 = −𝒙 + 𝟕
−𝟐𝒙 = 𝟔
𝒙 = −𝟑
(−𝟑, 10)
(𝟐, 5)
CHECK
|1 − 3(𝟐)| = |𝟐 − 7|
CHECK
|1 − 3(−𝟑)| = |−𝟑 − 7|
5=5
10 = 10
U1A L4 ANS Abs Value Equations
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