Question 59195: Solve for z:1/2 absolute value of z + 5=2 absolute value of z-10.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve for z:1/2 absolute value of z + 5=2 absolute value of z-10.
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(1/2)|z+5| = 2|z-10|
EQUATION: |z+5} = 4|z-10|
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Draw a number line.
Label z=-5 and z=10
This breaks the line into three intervals.
I: (-inf,-5)
II: (-5,10)
III: (10,inf)
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EQUATION is different in each of these intervals:
I: -(z+5)=-4(z-10)
z+5=4(z-10)
z+5=4z-40
3z=45
z=15
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II: (z+5)=-4(z-10)
z+5 = -4z+40
5z=35
z=7
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III: z+5=4(z-10)
same solution as in interval I
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Final Solution:
z=7 and z=15
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Comment: The changing value of the absolute components
results from the definition of absolute x
If x>=0, then absolute x= x
If x<0, then absolute x = -x
Cheers,
Stan H.
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