Question 66376: absolute value of x-1 -0.5 is less than or equal to (1/2)x+5
graph with points
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! absolute value of x-1 -0.5 is less than or equal to (1/2)x+5
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|x-1|-0.5 <=(1/2)x+5
|x-1|<=(1/2)x+5.5
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Comment: The absolute can have two meanings:
If x>=1 |x-1|=x-1
If x<1 |x-1|=-(x-1)
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So,
If x>=1, you get x-1<=(1/2)x+5.5
(1/2)x<=6.5
x<=13
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If x<1, you get -(x-1)<=(1/2)x+5.5
-x+1<=(1/2)x+5.5
(3/2)x>=-4.5
x>=-3
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Final solution:
-3<=x<=13
Cheers,
Stan H.
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