# Math Help - Absolutely Annoying (Absolute value)

1. ## Absolutely Annoying (Absolute value)

Hi MHF, stuck on a homework problem. I need to solve for a.

$|2a+8|=|2a-6|$

2. |a|= |b| reduces to two equations: a= b or a= -b.

|2a+ 8|= |2a- 6| reduces to 2a+ 8= 2a- 6 or 2a+ 8= -(2a- 6). Can you solve those (one of them has no solution).

3. Sketch these functions, you will see there is no solution.

4. Originally Posted by HallsofIvy
|a|= |b| reduces to two equations: a= b or a= -b.

|2a+ 8|= |2a- 6| reduces to 2a+ 8= 2a- 6 or 2a+ 8= -(2a- 6). Can you solve those (one of them has no solution).
So, I'm guessing $2a+8=2a-6$ would have no solution. $2a+8=-2a+6$ would come out to $a=-1/2$

Correct?

I was on the right track, just wasn't sure of myself.

5. yes you are correct

6. Originally Posted by pickslides
Sketch these functions, you will see there is no solution.
How is a= -1/2 not a solution?

7. Originally Posted by Fails_at_Math
So, I'm guessing $2a+8=2a-6$ would have no solution. $2a+8=-2a+6$ would come out to $a=-1/2$

Correct?

I was on the right track, just wasn't sure of myself.
Don't guess! If 2a+ 8= -2a+ 6, adding 2a to both sides gives 8= 6 which is NOT true. There is no value of a which makes it true. Yes, if a= -1/2,
then 2a+ 8= 2(-1/2)+ 8= -1+ 8= 7 and |7|= 7, while 2a- 6= 2(-1/2)- 6= -1- 6= -7 and |-7|= 7.

8. Originally Posted by Fails_at_Math

$|2a+8|=|2a-6|$
Both sides positives, so you can square them and then $32a+64=-24a+36,$ and it follows that $a=-\frac12.$