Rules
What do you do first to solve an Absolute Value Equation?
Get the Absolute Value bars by themselves
| d + 5 | = 9
What is { 4 , -14 }
| w + 9 | < 17
w< 8 and w> -26
| x - 6 | > 35
x> 41 , x<-29
How many equations should you have when solving absolute value?
Two
| a - 6 | = 10
What is { 16 , -4 }
2 | x + 5 | > 22
x< -16 , x>6
| t + 9 | - 8 < 5
x< 4 , x> -22
Absolute value equations can never be equal to this
A negative number
3 |4x - 1| - 5 = 10
What is { -1, 3/2 }
3 | 2a - 4 | < 0
No solution
8 | 5w - 1 | > 24
w > 4/5, w< -2/5
How do you set up the two absolute value equations?
One is positive on the right side and the other is negative
| p + 1 | + 10 = 5
What is { No Solution }
|2x - 3| = 4x - 1
What is { 2/3 }
A factory produces widgets whose length must be within 1.5 mm of an ideal length of 47 mm. A factory supervisor wants to mark rulers with the least and greatest acceptable length for each widget for workers to use in quality control inspections. Let ℓ be the length of the markings along the ruler. Write an absolute value inequality to represent this situation.
|ℓ - 47| </ 1.5
5| 3b - 10 | > 15
b> 13/3, b< 7/3
Describe how you know which way to shade the number line when doing absolute value inequalities.
Shade left for less than signs and shade right for greater than signs.
|3x + 2| = 4x + 5
What is { -1 }
6 |2x+5| = 6x + 24
What is { -3, -1} ?
You and your friends Jose and Sarah all live on the same street. You know that Jose lives five blocks away from you. Jose says that Sarah lives two blocks from him, but he didn’t say whether she lives closer to you than he does or further. Let b be the number of blocks Sarah might live from you. Write and solve an inequality.
|b - 5| </ 2
3</b</7
-5 | 3z + 8 | - 5 > -20
z> -5/3, z< -11/3