Question 145709: |16-3x|=|x|+3
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! |16-3x|=|x|+3
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The absolute value terms have a different meaning depending
on whether the variable expression is negative or not negative.
The break points for your equation are x = (16/3) and x = 0
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Draw a number line and mark x = (16/3) and x= 0.
Check for solutions in the three intervals formed by these values.
If x < 0 you get: 16-3x = -x + 3
2x = 13
x = 13/2
But x must be <0 so x=13/2 is not a solution.
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If 0<=x<16/3 you get: 16-3x = x + 3
4x = 13
x = 13/4
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If x > 16/3 you get 3x-16 = x + 3
2x = 19
x = 19/2
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Final Answer: x = 13/4 or x = 19/2
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Cheers,
Stan H.
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