- #1
fatcrispy
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Homework Statement
Given: |A|+A+B=15 and A+|B|-B=13. What is A+B equal to? Give all possibilities.
Homework Equations
The Attempt at a Solution
I solve for both absolute variables. So,
A=15-A-B or A=A+B-15
and
B=13-A+B or B=A-B-13
Firstly, I solve for A.
A+A=15-B
2A=15-B
A=[tex]\frac{15-B}{2}[/tex]
and
A-A=B-15
0=B-15
B=15
Plug them back into the original eq. to see if it works.
|[tex]\frac{15-B}{2}[/tex]|+[tex]\frac{15-B}{2}[/tex]+B=15
|[tex]\frac{15-B}{2}[/tex]|=15-B-[tex]\frac{15-B}{2}[/tex]
|[tex]\frac{15-B}{2}[/tex]|=+/- [tex]\frac{15-B}{2}[/tex]
So that works. But when I plug in B=15 into the original eq. it doesn't.
So far, I have A=[tex]\frac{15-B}{2}[/tex]. Next, I solve for B.
B-B=13-A
0=13-A
A=13
and
B+B=A-13
2B=A-13
B=[tex]\frac{A-13}{2}[/tex]
So, I plug in B into the original equation(the second one given).
Plugging in A=13 just comes out to B=+/- B.
Plugging in B=[tex]\frac{A-13}{2}[/tex] results in
[tex]\frac{A-13}{2}[/tex]=+/- [tex]\frac{A-13}{2}[/tex].
So, when the problem asks for A+B, how do I add them? Do I do:
A+B=[tex]\frac{15-B}{2}[/tex]+[tex]\frac{A-13}{2}[/tex] ?
Please help! Thanks.