1. How to work Absolute Value equations and inequalities
by: Cole, Hannah,
Robert, and Peyton

2. Let’s start with a few
practice problems

3. Solve for a
|2a+6|=16
You read this: the absolute value of 2a plus 6 equals 16.
The first thing you do is split this up into two equations 2a+6=16 and 2a+6=-16.
The second thing you do is work the first one:2a+6=16. First, subtract 6 from both sides to get 2a=10. Second, Get the a alone by dividing both sides by 2 and you get a=5.
The third thing you do is work the second one: 2a+6=-16. First, subtract 6 from both sides to get 2a=-22. Second, get the a alone by dividing both sides by 2 and you get -11.
The solution set to this problem is {5,-11}

4. |2a-10|>22 Graph the following inequality -6 10 16 -5
First, you need to solve the inequality.
You do this by splitting it up into two different inequalities: 2a-10>22 and 2a-10<-22.
The second thing you do is work the first inequality. First, add 10 to both sides to get 2a>32. Next, you get a alone by dividing both sides by 2 to get a>16
The third thing you do is solve the second inequality. First, add 10 to both sides to get 2a<-12. After that, you divide both sides by 2 to get a<-6.
The last thing you do is graph this by getting the two answers and graphing them. So you graph a>16 and a<-6.
To decide which way you shade darker, you look at which way the inequality symbol is pointing. That is the way you shade in.
The graph should look like this -6 10 16 -5

5. Shows the solution set to
Which of the following
Shows the solution set to
|2b+3|=7?
A. {3,6}
B. {0,1}
C. {2,-5}
D. No solution

6. If you guessed C, YOU ARE CORRECT!!!!!!
CONGRATULATIONS!!!!

7. Now let’s see how you got C.
First, you split it up into two equations like I have taught you in previous problems, so when you did that, you had 2b+3=7 and 2b+3=-7.
After that, you worked the first equation by subtracting 3 from both sides to get 2b=4. Next you got b alone by dividing both sides by 2 and got a=2.
Then, you worked the second equation by subtracting 3 from both sides and got 2b=10. Next you got b alone by dividing both sides by 2 and got a=-5.
You got C. Good Job!!!!!!!!!!!!!!!!!!!

8. lines correctly graphs
Which of the following
lines correctly graphs
the equation |a-4|=7? A. -3 11 B. -3 11 C. -3 11 D. -3 11

9. If you got A.
You are correct.
Congratulations!!!
Good Job!!!!

10. First, you split the equation up into two and got a-4=7 and a-4=-7.
Next, you worked the first equation by adding 4 to both sides and getting a=11.
Then, you worked the second equation by adding 4 to both sides and getting a=-3.
Finally you looked at which graph resembled your solution set. Since there were no arrows pointing anywhere or anything, you just had to choose the one that plotted your tow points 11 and -3.
The graph that resembled it was A.

11. Solve for x
|2x+3|=57
First, you set up two equations 2x+3=57 and 2x+3=-57.
Second, you work the first equation by subtracting 3 from both sides to get 2x=54. Next, divide both sides by 2 and get x=27.
Third, you work the second equation by subtracting 3 from both sides to get 2x=-60. Next, divide both sides by 2 to get x=-30
The solution set to this problem is {27,30}.

12. You are
now an absolute
value Genius!!!!!!