This week in class we discussed how to solve absolute value equations and equalities.
Example:
|2x-6|= 4
2x-6= 4 or 2x-6= -4
. .
. .
x = 5 x = 1
We have learned 3 different "kinds" of equations that are each solved and graphed differently
1) Equal To ("OR")
2) Greater Than/Greater Than Equal To ("OR")
3) Less Than/Less Than Equal To ("AND")
( p.71)
1) | 4s + 5 | = 2
4s + 5 = 2 or 4s + 5 = -2
4s = -3 4s = -7
s = - 3/4 s= -4/7
In this problem the answer is either of the two answers but nothing else
2) | 2y + 3 | > 11
2y + 3 > 11 or 2y + 3 < -11
2y > 8 2y < -14
y > 4 y < -7
In this problem the answer is everything either above or below the two solutions to the equation excluding the solutions.
3) | k - 7/2 | < 5/2
k - 7/2 < 5/2 and k - 7/2 > - 5/2
k < - 1 k > -6
In this problem the answer is in between the two solutions to the equation excluding the answers
Reminder: In all of these, the original equation is written out into two different equations with the absolute value, the signs are switched in one of them, and they are solved separately.
For problems like these: 2 < | x | < 4
Separate the equation into two different equations
| x | > 2
and
| x | < 4
Then solve them separately resulting most of the time in 4 answers instead of 2
x > 2 x < 4
and
x < -2 x > -4
Tips and Tricks:
|4f +18| = 0 - This is a trick problem because there will be only one answer because 0 is neither negative nor positive
- Always write the absolute value first in the order of the equation
This can all be found in the book from pages 71-73
Hope this was helpful :)
Elise
Great post Elise!
ReplyDeleteSorry this comment is so late, but I think that this post is great and it clearly demonstrates each different theme/version of using absolute value in equations and equalities. It is also very organized, using pictures and different colours, to show the different facts and variations!
Good Post over all!! :)
Also the comic on the end is a nice funny touch!
Elise, Your post is well organized and does a nice job outlining the different scenarios you might encounter when solving absolute value equations and inequalities. The examples are accurately done and cover all three types. Including a real number line graph of each solution (particularly in examples 2, 3, and the last one) would have offered yet another way to "see" the final solution. Also, sometimes, with multiple "and's" and "or's" the final solution can be written in a more condensed way once the region is graphed. This is the case in your last example - by graphing you can see that the only x values that work are between -4 and -2 (inclusive) and between 2 and 4 (inclusive). Finally, I like your tip in green, your reference to the pages in the book, and the math comic you included. Overall, nicely done.
ReplyDeleteI really liked this post. My favorite thing about this post was how spaced this was. I think it was easier to read everything and understand. It also gave time so the reader could process what was being said. I think that all the information that was given was important. Overall Great Job!
ReplyDelete