SOLUTION: I am trying to figure out this equation. 8-|x+2|=5 I am using my math lab and tried to use the view an example solution which ended up being the exact same equation and I kn

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Question 830963: I am trying to figure out this equation.
8-|x+2|=5
I am using my math lab and tried to use the view an example solution which ended up being the exact same equation and I know the answer is X=-5,1 but I dont understand when you try to get the absolute value by its self how you Isolate with the way the equation is written. I know that you could read the equation like this 8(-1)|x+2|=5 but when I look at the example the answer they recieve is |x+2|=3 and I am very confused because it did not show me the steps on how it got to this point. can you please help me understand this process. Thank you!
Found 2 solutions by josgarithmetic, rothauserc:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
8-|x+2|=5 and 8(-1)|x+2|=5 are not the same equation; they are not equivalent. That could be what is confusing you. The second of those two would be -8*|x+2|=5.

If you are given the first equation:
8-abs%28x%2B2%29=5
-abs%28x%2B2%29=5-8
-abs%28x%2B2%29=-3
abs%28x%2B2%29=3
-
Consider the conditions of x+2 being positive or zero; and of being negative.
-
x%2B2%3E=0, then abs%28x%2B2%29=x%2B2=3
x=3-2
highlight%28x=1%29
-
x%2B2%3C0, then abs%28x%2B2%29=-x-2=3
x%2B2=-3
x=-3-2
highlight%28x=-5%29
-
-
You SHOULD check each of these solutions for x in the original (given) equation to see if either of them fails as a solution. x=-5 will work. Actually, x=1 will also work.


Note that in most absolute value EQUATIONS, you can treat the absolute value as a variable until it is isolated to be analyzed more closely.

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
8-|x+2|=5
subtract 8 from both sides of =
-|x+2| = -3
divide both sides of = by -
|x+2| = 3
there are two cases
1) x+2 = 3
x = 1
2) -x-2 = 3
-x = 5
x = -5
therefore x = -5, 1