For what value of x does |x-4| = 4-x ?
I solved it as follows:
Case1: +(x-4)= 4-x
=> x-4 = 4-x
=> x=4
Substituting 4 in |x-4| = 4 -x
0=0
True
So x=4 is valid
Case2: -(x-4) = 4-x
-x = -x
Lost here...Is this right?
The right answer is, for all x<=4. But, how? I only got x=4.
Some absolute value fundamentals would help clarify this problem for me.
Thanks in advance.
Absolute Value Problem
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- iwillsurvive101
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Definition of |x|iwillsurvive101 wrote:For what value of x does |x-4| = 4-x ?
Case2: -(x-4) = 4-x
-x = -x, Lost here...Is this right?
The right answer is, for all x<=4. But, how? I only got x=4.
For any real number a the absolute value or modulus of a is denoted by |"‰a"‰| (a vertical bar on each side of the quantity) and is defined as
|"‰a"‰| = a, if a>0 and
|"‰a"‰| = -a, if a<0
So here,
|x-4| = 4-x;
|x-4| = -(x-4;
if y = x-4,
|"‰y"‰|=-y,
From the definition of |y| if |"‰y"‰|=-y, y < 0,
=> x-4<0
=> x<4
Anil Gandham
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- iwillsurvive101
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Thanks Mr. Quant, appreciate the detailed response. I was close, but just wanted to conceptually take-it-in ![Smile :-)](./images/smilies/smile.png)
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- neelgandham
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I am glad I could help. Thanks for the kind words. Let me know if you need any further help! and YES you will survive ![Smile :)](./images/smilies/smile.png)
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Anil Gandham
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4-x is the DIFFERENCE between 4 and x.For what values of x does |x-4| = 4-x?
A DIFFERENCE can be negative, 0, or positive.
|x-4| is the DISTANCE between x and 4.
A DISTANCE must be greater than or equal to 0.
For the DIFFERENCE between two values to be equal to the DISTANCE between the two values, the DIFFERENCE -- like the DISTANCE -- must be greater than or equal to 0:
4-x ≥0
4 ≥ x.
Thus, |x-4| = 4-x when x≤4.
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