Name _________________________
Due Date _____________________
Activity 3.1: Solving Absolute Value Equations Homework
1. What is the absolute value of a number?
2. Solve or evaluate.
a) |−7|
b) |7|
c) |4 − 9|
3. What are the possible values of x that would satisfy the equation … |𝑥| = 7 ?
4. Is it possible to have … |𝑥| = −2 ?
5. How many solutions are there for absolute value equations?
To Solve Equations with Absolute Value signs:
1. Isolate the Absolute Value
2. Set up 2 Equations – Get rid of the absolute value sign by setting everything in the absolute value equal to a
positive and a negative value.
3. Solve the two equation
Example:
|𝑥 − 2| = 5
(positive)
𝑥−2=5
+ 2 +2
x = 7
𝑥 − 2 = −5
+2 +2
x = –3
(negative)
1
Both 𝑥 = 7 and – 3 are solutions to the equation: |𝑥 − 2| = 5 .
Check your answers by putting them back into the original equation.
|𝑥 − 2| = 5
𝑥 = −7 |7 − 2| = |5| = 5
𝑥 = −3 |−3 − 2| = |−5| = 5
6. Solve the 2 equations to find the solutions and check:
|𝑥 − 5| + 2 = 9
–2 –2
|𝑥 − 5| = 7
(positive)
𝑥−5=7
𝑥 − 5 = −7
(negative)
Check:
Practice: Please solve and check each absolute value equation.
7. |𝑥 − 3| = 8
Check:
9. |𝑥 + 1| − 7 = 10
Check:
8. |𝑥 + 4| = 6
Check:
2
10. |𝑥 − 5| + 2 = 4
13. |1 − 6𝑛| + 3 = 46
Check:
Check:
11. |2𝑥 − 3| = 5
14
3𝑣−2
5
=4
Check:
Check:
12. |3𝑥 − 1| + 4 = 9
Check:
3
Part 2: Solve each equation. Be sure to check your solutions by substituting each answer into the original
equation. Make sure you have 2 answers.
a.
x6 8
Check:
c.
 9 x  64
Check:
b. x  2  8
Check:
d.  7 x  4  18
Check:
4
e. 4 x  4  28
f. 5 n  10  10
Check:
g. 1  6n  3  46
Check:
Check:
h.
3v  2
5
4
Check:
5