document.write( "Question 708722: Respected Sir,\r
\n" ); document.write( "\n" ); document.write( " My Question is :\r
\n" ); document.write( "\n" ); document.write( "If |x − 2| + |x − 3| = 7 then x \r
\n" ); document.write( "\n" ); document.write( "Please Explain me the Doubt clearly in detail ?
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Algebra.Com's Answer #436215 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
The two solutions are $\"highlight%28x=6%29\"$ and $\"highlight%28x=-1%29\"$
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\n" ); document.write( "For $\"2%3C=x%3C=3\"$ , $\"x-2%3E=0\"$ and $\"x-3%3C=0\"$ , then
\n" ); document.write( " $\"abs%28x-2%29%2Babs%28x-3%29=%28x-2%29-%28x-3%29=x-2-x%2B3=1\"$
\n" ); document.write( "The expression $\"abs%28x-2%29%2Babs%28x-3%29\"$ cannot equal $\"7%7D%7D%0D%0Aand+we+do+not+find+a+solution+in+the+interval+where+%7B%7B%7B2%3C=x%3C=3\"$ \r
\n" ); document.write( "\n" ); document.write( "So either $\"x%3E3\"$ , making $\"x-2\"$ and $\"x-3\"$ both positive adding to $\"7\"$
\n" ); document.write( "or $\"x%3C2\"$ , making $\"x-2\"$ and $\"x-3\"$ both negative,
\n" ); document.write( "adding to $\"-7\"$
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\n" ); document.write( "For $\"x%3E3\"$ :
\n" ); document.write( " $\"abs%28x-2%29%2Babs%28x-3%29=%28x-2%29%2B%28x-3%29=x-2%2Bx-3=2x-5\"$
\n" ); document.write( "We solve $\"2x-5=7\"$
\n" ); document.write( " $\"2x-5=7\"$ --> $\"2x=7%2B5\"$ --> $\"2x=12\"$ --> $\"x=12%2F2\"$ --> $\"highlight%28x=6%29\"$
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\n" ); document.write( "For $\"x%3C2\"$ :
\n" ); document.write( " $\"abs%28x-2%29%2Babs%28x-3%29=-%28x-2%29-%28x-3%29=-x%2B2%2Bx%2B3=-2x%2B5\"$
\n" ); document.write( "So $\"-2x%2B5=7\"$ <--> $\"2x-5=-7\"$
\n" ); document.write( "We solve $\"2x-5=-7\"$
\n" ); document.write( " $\"2x-5=-7\"$ --> $\"2x=-7%2B5\"$ --> $\"2x=-2\"$ --> $\"x=-2%2F2\"$ --> $\"highlight%28x=-1%29\"$ \n" ); document.write( "

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