SOLUTION: Please help me with this problem: Solve the following absolute value inequalities: The absolute value of (x+1)is less than or equal to the absolute value of (x-3). I'm sor

Algebra ->  Algebra  -> Inequalities -> SOLUTION: Please help me with this problem: Solve the following absolute value inequalities: The absolute value of (x+1)is less than or equal to the absolute value of (x-3). I'm sor      Log On

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Question 92613: Please help me with this problem:
Solve the following absolute value inequalities:
The absolute value of (x+1)is less than or equal to the absolute value of (x-3).

I'm sorry I don't know how to key in a problem like that. I know how to solve a problem with absoulute value on one side, but does that same concept apply? Do you separate each side? I really have no idea where to go from here. Any help would be GREATLY appreciated.

~Amanda
Found 2 solutions by stanbon, psbhowmick:
Answer by stanbon(57387) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me with this problem:
Solve the following absolute value inequalities:
The absolute value of (x+1)is less than or equal to t
he absolute value of (x-3).
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graph%28400%2C300%2C-10%2C10%2C-10%2C10%2Cabs%28x%2B1%29%2Cabs%28x-3%29%29
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Solution: x<=1
============
Cheers,
Stan H.

Answer by psbhowmick(529) About Me  (Show Source):
You can put this solution on YOUR website!
|x+1| => |x-3|

Let us consider different cases with different sets of values of 'x':
1. x <= -1; then the inequality becomes: -(x+1) => -(x-3) i.e. -3 >= 1 which is absurd
2. -1<= x <= 3; then the inequality becomes: x+1 => -(x-3) i.e. x >= 1
3. 3<= x; then the inequality becomes: x+1 => x-3 i.e. 1 >= -3 which is true

So, the solution is: x >= 1.