Help me !!!! For the following exercises solve the equation below and express the answer using set notation. l 6-x l = 5 But the answer is 1, 1/2 , -2. How did they get these answers ?

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Help me !!!! For the following exercises solve the equation below and express the answer using set notation. l 6-x l = 5 But the answer is 1, 1/2 , -2. How did they get these answers ?

Mathematics
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This is what i did : l 6-x l = 5 -x +6 = 5 x = 1 ? please tell me if i am correct or wrong ?
you are correct
yea x=1 or x=11 are the answers :) u are 100% correct :D

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Other answers:

I would not say you are 100% correct. You are 50% correct. Remember \(|A|=b\) means \(a=b\) and \(-a=b\) So you have \(6-x=5\) which gives \(x=1\) But we must also consider \[-(6-x)=5\] which leads to \(x=11\).
yes
But we are all actually wrong as it asked for the answer in set notation, so the answer is \(\{1,11\}\)
so the interval notation is from smallest to biggest ?
\[\left\{ 1,11 \right\}\]means that there r 2 elementary solutions 1 and 11 :)
when ever you see the modulus you have to consider the negative and positive values means less then the positive value and greater than the negative value like that \[\left| x \right|=4\] it means -44
oh okay . Got it !! Thank Yous !!! I have another equation bur under same category. l 4x-2 l =11 x= 13/4 and x = -9/4 ? interval notation : { -9/4 , 13/4 }
You are correct
for my second problem ?
yes! :) now you got the concept buddy
now close this question and ask new :)
Okay. I checked my solution book and it did include the - 9/4 ?
i mean 9/4 .
wait in book -9/4 is not given ?
yes , the interval notation says { 9/4 , 13/4}
no it will be -9/4 to 13/4 not 9/4
Okay . Thanks.
np

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