1. Solving Absolute Value Equations-6 -5 -4 -3 -2 -1 1 2 3 4 5 6
Medina

2. Definition
Absolute Value– The absolute value of a number is the distance from zero.
Since distance can not be negative, the absolute value of a number is always positive.
However, that does not mean that an absolute value equation will only have positives value for solutions.
Absolute value equation have two solutions because you can move in two different directions on the number line, you can move to the left or right on the number line from zero.
Medina

3. Absolute Value– The absolute value of a number is the distance from zero.
Medina

4. The absolute value of x is the distance from zero. If | x | = -5
Absolute Value– The absolute value of a number is the distance from zero
The absolute value of x is the distance from zero.
If | x | = -5
Start Here
Think about it
Wait!!!! 1 2 3 4 5 6 -1 -2 -3 -4 -5 -6
Always check!
Can we take -5 steps?
No, distance is always positive
therefore its No Solution
Medina

5. Solving Absolute Value Equations
Isolate the absolute value sign
Separate the equation into the two possible distances from zero.
Solve for the variable
Check solutions
Medina

6. Solving Absolute Value Equations
1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
3. Solve for the variable
4. Check solutions
Medina

7. Solving Absolute Value Equations
1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
3. Solve for the variable
4. Check solutions
D U +7
- 7
Medina

8. Solving Absolute Value Equations
1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
3. Solve for the variable
4. Check solutions
D U •2 ÷2
Medina

9. Solving Absolute Value Equations
1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
3. Solve for the variable
4. Check solutions
D U •2 -8 +8 ÷2
Medina

10. Solving Absolute Value Equations
1. Isolate the absolute value sign
2. Separate the equation into the two possible equations
3. Check solution!!
D U
•(-2)
÷(-2)
Think about it…
Can we take -4 steps?
No, distance is always positive
Medina

11. Writing Absolute Value Equations
Has to have an equal sign
Has to have an absolute value symbol
Has to have a variable
Staring
Value
Minimum
Value
𝑥−# =#
Maximum
Value
“Distance” that can vary from the starting value
Medina

12. Writing Absolute Value Equations
To fit correctly, the width of a machine part can vary no more than 0.01 millimeter from 2.5 millimeters. Write an absolute value equation to find the minimum and maximum width of the part.
Minimum
Value
Staring
Value
Absolute Value Equation:
𝒘 = 𝒘𝒊𝒅𝒕𝒉 𝒐𝒇 𝒎𝒂𝒄𝒉𝒊𝒏𝒆 𝒑𝒂𝒓𝒕
− =
2.5
0.01 𝑤
“Distance” that can vary from the starting value
Maximum
Value
Medina

13. Writing Absolute Value Equations
The distance between the Earth and the sun is not constant, because Earth’s orbit around the sun is an ellipse whose path vary 1.55 miles (in millions) from miles. What is the minimum and maximum distance between the Earth and the sun?
Minimum
Value
Staring
Value
Absolute Value Equation:
𝒅 =𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒇𝒓𝒐𝒎 𝑺𝒖𝒏 𝒕𝒐 𝑬𝒂𝒓𝒕𝒉
− = 𝑑
92.95
1.55
“Distance” that can vary from the starting value
Maximum
Value
Medina

14. Writing Absolute Value Equations
The shoulder height of the shortest miniature poodle is 10 inches. The shoulder height of the tallest poodle is 15 inches. What is the absolute value equation that has these two shoulder heights for poodles as its solutions?
Staring
Value
Minimum
Value
I have the minimum and maximum values, could I figure out the starting value and distance from starting value?
Absolute Value Equation:
𝒉=𝒔𝒉𝒐𝒖𝒍𝒅𝒆𝒓 𝒉𝒆𝒊𝒈𝒉𝒕 𝒐𝒇 𝒑𝒐𝒐𝒅𝒍𝒆𝒔
− = ℎ
12.5 ?
2.5 ?
Yes!!
Maximum
Value
“Distance” that can vary from the starting value
Staring
Value
Minimum
Value
Maximum
Value 10 11 12 13 14 15 16 9 8 7 6 5 4
Total distance between height is 5 inches.
2.5
2.5
Starting distance has to be in the middle.
Now, I can find the distance from the starting value by dividing the total distance into two part (5÷ 2).
Medina