Solving Absolute Value Equations: plot solutions to | 2n | = 6

brazil820

New member
Joined
Oct 20, 2016
Messages
4
Hey everyone, could anyone help me with solving Absolute Value Equations? I understand what Absolute Value means but the equations I do not understand at all. Here is an example:

attachment.php
 

Attachments

  • equations1.png
    equations1.png
    11 KB · Views: 21
Hey everyone, could anyone help me with solving Absolute Value Equations? I understand what Absolute Value means but the equations I do not understand at all. Here is an example:

. . . . .Plot the possible values of n that make | 2n | = 6 a true statement.
Since you don't know the topic, the first step is to learn it. We can't teach lessons within this environment, but there are loads of lessons available, such as the ones in this lising.

Please study at least three lessons from the listing. Then please attempt the exercise. If you get stuck, you can then reply with a clear listing of your thoughts and efforts, at which point we can try to help you get unstuck. Thank you! ;)
 
Hey everyone, could anyone help me with solving Absolute Value Equations? I understand what Absolute Value means but the equations I do not understand at all. Here is an example:

attachment.php
The problem is asking what number or numbers, if any that you can put between the absolute values bars to get 6. Note that my question has NOTHING to do with 2n. Just decide what number or numbers, if any when you take the absolute value of them would equal 6. Then let 2n = those numbers (one at a time) and solve for n.
 
It would be a good idea to start with the definition of "absolute value": |x|= x if x is greater than or equal to 0, |x|= -x if x is less than 0.

So |2n|= 2n if n is greater than or equal to 0, |2n|= -2n if x< 0.

Case 1: if n is greater than or equal to 0, then |2n|= 2n= 6 so n= 3. That is positive so is a valid solution.
Check: 2(3)= 6 which is positive so |2(3)|= |6|= 6.

Case 2: if n< 0, then |2n|= -2n= 6 so n= -3. That is negative so is a valid solution.
Check: 2(-3)= -6 which is negative so |2(-3)|= |-6|= 6.

The two numbers, 3 and -3, satisfy |2n|= 6.
 
Thank you for the help so far! We appreciate it. In response to the first answer, my daughter understands what Absolute Value is but was having trouble working on these practice problems, which is why we came here for help in understanding them.

We now understand how this problem is solved and thank you again. :)
 
Last edited by a moderator:
You keep saying that your daughter "understands what absolute value means" but your questions don't show that. If x= 6, what is |x|? If x= -6, what is |x|? What values of x satisfy |x|= 6?

Does your daughter understand the definition of |x|: that \(\displaystyle |x|= x\) if \(\displaystyle x\ge 0\) and \(\displaystyle |x|= -x\) if \(\displaystyle x< 0\)?

Does you daughter understand that if |2x|= a then either 2x= a or 2x= -a?
 
Top