Question 15489: How do you solve absolute value equations?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! It is quite simple procedure . Let us take one simple equation to illutrate the principle involved Say...Solve |x+4|=5
|x+4| is read as Absolute value or MOD of x+4 .this means that whether x+4 is negative or positive ,we should take its positive value .that is if x+4 turns out to be positive then take its value as such that is x+4 only; and if x+4 turns out to be negative ,then take its negative value so that we get a positive value only.that is in that case we should take -(x+4) as its value. so this means we have 2 cases and hence 2 equations and so 2 solutions . in these problems we should therefore write the 2 cases and 2 equations first.
case1...x+4 is positive ..then |x+4|=x+4 = 5 or x=5-4 =1 is the answer.
case2...x+4 is negative ..then |x+4|=-(x+4) = 5 or -x=5+4 =9 or x=-9 is the answer.
Hence we should write the solution as x=1 or -9 ........answer.
So now you see that if x+4=5 is the problem ,we will get only one answer namely x=1 ; but if the problem is |x+4|=5 , we get 2 answers namely x=1 or -9 .hope you understood .
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