2-5 ABSOLUTE VALUE
EQUATIONS
Goals:
•
Evaluate absolute value expressions
•
Solve absolute value equations.
Eligible Content:
A1.1.1.3.1 / A1.1.2.1.1 / A1.1.2.1.2 / A1.1.2.1.3
VOCABULARY

Absolute Value – the distance from 0.
EVALUATE EACH EXPRESSION
1.
2.
3.
4.
5.
6.
7.
−17
39
5−8
− 28
− −12
𝑚 + 6 − 14 when m = 4
15 − 𝑥 + 7 when x = – 3
LOOK AT |X|= 5

What numbers can x be?

x can be 5 or x can be -5

So x = 5 or x = -5
Check it!
|5| = 5 AND |-5|= 5
Every absolute value problem has 2
answers!
 You must do 2 problems to find the 2 answers!!!

SOLVE: 𝑥 − 2 = 5
The expression (x – 2) can be equal to 5 or –5!!!
x – 2 is positive
x – 2 is negative
x–2=5
+2 +2
x=7
x – 2 = –5
+2 +2
x = –3
So x = 7 or x = –3
EXAMPLES
1.
|x – 4|= 9
x = 13 or x = -5
2.
|2x + 2|= 8
x = 3 or x = -5
3.
|–4x – 7|= 12
x = -4.75 or x = 1.25
4.
|p + 6| = –5
no solution
Solve |2x + 3| = 5. Graph the solution set.
A. {1, –4}
B. {1, 4}
C. {–1, –4}
D. {–1, 4}
Solve |x – 3| = –5.
A. {8, –2}
B. {–8, 2}
C. {8, 2}
D.
PRACTICE

Page 105 #1-9
WRITE AN ABSOLUTE VALUE EQUATION



Find the midpoint between two points
Find the distance to the midpoint from each
point.
Write equation:
𝑥 − midpoint = distance from midpoint to points
EXAMPLES
Write an equation for each graph.
1.
𝑥−1 =3
2.
𝑥−2 =6
3.
𝑥+5 =2
Write an equation involving the absolute value
for the graph.
A. |x – 2| = 4
B. |x + 2| = 4
C. |x – 4| = 2
D. |x + 4| = 2
WORD PROBLEM #1
The temperature of a snake enclosure should be
about 80°F, give or take 5°. Use an absolute value
equation to find the minimum and maximum
temperature.
𝑥 − 80 = 5
x = 75 or x = 85
Minimum: 75°
Maximum: 85°
WORD PROBLEM #2
The average January temperature in a northern
Canadian city is 1°F. The actual temperature may
be about 7° warmer or colder. Use an absolute
value equation to find the minimum and maximum
temperature.
𝑥−1 =7
x = –6 or x = 8
Minimum: –6°
Maximum: 8°
WEATHER The average temperature for
Columbus on Tuesday was 45ºF. The actual
temperature for anytime during the day may
have actually varied from the average
temperature by 15ºF. Solve to find the maximum
and minimum temperatures.
A. {–60, 60}
B. {0, 60}
C. {–45, 45}
D. {30, 60}
HOMEWORK

Page 106 #14-30 even
#33-36