document.write( "Question 59195: Solve for z:1/2 absolute value of z + 5=2 absolute value of z-10. \n" ); document.write( "
Algebra.Com's Answer #40585 by stanbon(75887)\"\" \"About 
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Solve for z:1/2 absolute value of z + 5=2 absolute value of z-10.
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\n" ); document.write( "(1/2)|z+5| = 2|z-10|
\n" ); document.write( "EQUATION: |z+5} = 4|z-10|
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\n" ); document.write( "Draw a number line.
\n" ); document.write( "Label z=-5 and z=10
\n" ); document.write( "This breaks the line into three intervals.
\n" ); document.write( "I: (-inf,-5)
\n" ); document.write( "II: (-5,10)
\n" ); document.write( "III: (10,inf)
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\n" ); document.write( "EQUATION is different in each of these intervals:
\n" ); document.write( "I: -(z+5)=-4(z-10)
\n" ); document.write( " z+5=4(z-10)
\n" ); document.write( " z+5=4z-40
\n" ); document.write( " 3z=45
\n" ); document.write( " z=15
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\n" ); document.write( "II: (z+5)=-4(z-10)
\n" ); document.write( " z+5 = -4z+40
\n" ); document.write( " 5z=35
\n" ); document.write( " z=7
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\n" ); document.write( "III: z+5=4(z-10)
\n" ); document.write( " same solution as in interval I
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\n" ); document.write( "Final Solution:
\n" ); document.write( " z=7 and z=15
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\n" ); document.write( "Comment: The changing value of the absolute components
\n" ); document.write( "results from the definition of absolute x
\n" ); document.write( "If x>=0, then absolute x= x
\n" ); document.write( "If x<0, then absolute x = -x
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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