document.write( "Question 1049350: Please help me to answer this question. Solve $\"%28x%29abs%285x-1%29+=+%282x-4%29\"$ \n" ); document.write( "

Algebra.Com's Answer #664937 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Use the definition of the absolute value function to break up the function into two functions.
\n" ); document.write( "1. $\"x%285x-1%29=2x-4\"$ when $\"5x-1%3E=0\"$
\n" ); document.write( "2. $\"-x%285x-1%29=2x-4\"$ when $\"5x-1%3C0\"$
\n" ); document.write( "So then,
\n" ); document.write( "Using eq. 1,
\n" ); document.write( " $\"5x%5E2-x=2x-4\"$
\n" ); document.write( " $\"5x%5E2-3x%2B4=0\"$
\n" ); document.write( "No real solutions.
\n" ); document.write( "Using eq. 2,
\n" ); document.write( " $\"-5x%5E2%2Bx=2x-4\"$
\n" ); document.write( " $\"-5x%5E2-x%2B4=0\"$
\n" ); document.write( " $\"5x%5E2%2Bx-4=0\"$
\n" ); document.write( " $\"%28x%2B1%29%285x-4%29=0\"$
\n" ); document.write( "Two solutions:
\n" ); document.write( " $\"x%2B1=0\"$
\n" ); document.write( " $\"x=-1\"$
\n" ); document.write( "and
\n" ); document.write( " $\"5x-4=0\"$
\n" ); document.write( " $\"5x=4\"$
\n" ); document.write( " $\"x=4%2F5\"$
\n" ); document.write( "However we have to check our original condition,
\n" ); document.write( " $\"5x-1%3C0\"$
\n" ); document.write( " $\"5x%3C1\"$
\n" ); document.write( " $\"x%3C1%2F5\"$
\n" ); document.write( "So then only $\"x=-1\"$ would be a solution.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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