# 2-5 Absolute Value Equations

```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
 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&deg;F, give or take 5&deg;. Use an absolute value
equation to find the minimum and maximum
temperature.
𝑥 − 80 = 5
x = 75 or x = 85
Minimum: 75&deg;
Maximum: 85&deg;
WORD PROBLEM #2
The average January temperature in a northern
Canadian city is 1&deg;F. The actual temperature may
be about 7&deg; 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&deg;
Maximum: 8&deg;
WEATHER The average temperature for
Columbus on Tuesday was 45&ordm;F. The actual
temperature for anytime during the day may
have actually varied from the average
temperature by 15&ordm;F. 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
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