1. 4.4 Solving Absolute Value Equations
Solve and write absolute value equations in one variable

2. Warm-up
Find the equation of the line that goes through (2, -1) and is perpendicular to the line with equation x – 3y = 7.
A. B. C. D.
A driver’s education consists of a total of 46 hours of classroom instruction, driving, and observation. You must spend 3 times as much time in the classroom as driving, and 4 hours longer driving than observing. How much time do you spend driving?
A. B. C. D.
6 hours
10 hours
14 hours
30 hours
A football kicker scores 1 point for each extra point and 3 points for each field goal. One season, a kicker made 34 extra points and scored a total of 112 points. How many field goals did the kicker make?
A. B. C. D. 13 26 48 78

3. The absolute value of x can be defined algebraically as follows:
The absolute value of a number x, written , is the distance the number is from 0 on the number line.
Because distances are always positive or zero, the absolute value of a number cannot be negative.
The absolute value of x can be defined algebraically as follows:
If x is a positive number then
If x is zero then
The expression –x represents the opposite of x which when x is negative, -x is positive
If x is a negative number then

4. The absolute value equation
where c > 0 can have two possible value that make the statement true:
A positive value c and a negative value c.
Example.
x = 4 or x = -4
No solution

5.   Solve an absolute value equation 3 – 4x = 11 3 – 4x = -11 -4x = 8or
3 – 4x = -11
-4x = 8
-4x = -14
x = -2
Check  

6.   Solve an absolute value equation
You must 1st isolate the absolute value on one side of the equation
2x – 8 = 6 or
2x – 8 = -6
2x = 14
2x = 2
x = 7
x = 1
Check  

7. Write an absolute value equation
Write an absolute value equation that has -6 and 2 as a solution.
Locate the midpoint on the graph • •
The graph of each solution is 4 units from the midpoint, -2. The distance between a number x and -2 on the number line is
midpoint
distance

8. Write an absolute value equation
Write an absolute value equation that has -3 and 5 as a solution.
Find the distance from the midpoint to one of the solutions.
Find the midpoint:
Larger solution – midpoint
= 5 – 1 =4
The distance is 4

9. Write an absolute value equation
A runner has the times of 41.5 seconds and 43.7 seconds for a quarter mile. Write an absolute value equation that has those two times as its solutions.
=42.6
=1.1
The midpoint is at 42.6 which is 1.1 units from each point

10. What is (are) the solution(s) of
A. B. C. D.
Check:

11. Assignment
worksheet