document.write( "Question 116169: Whst is the absolute value of |x+6|=2x? \n" ); document.write( "

Algebra.Com's Answer #84478 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
The absolute value function has two values and you have to solve for both.
\n" ); document.write( "When (x+6)>0, then
\n" ); document.write( " $\"abs%28x%2B6%29=x%2B6\"$
\n" ); document.write( " $\"x%2B6=2x\"$
\n" ); document.write( " $\"x=6\"$
\n" ); document.write( "When (x+6)<0, then
\n" ); document.write( " $\"abs%28x%2B6%29=-%28x%2B6%29\"$
\n" ); document.write( " $\"-%28x%2B6%29=2x\"$
\n" ); document.write( " $\"-x-6=2x\"$
\n" ); document.write( " $\"3x=-6\"$
\n" ); document.write( " $\"x=-2\"$
\n" ); document.write( "Check your answers.
\n" ); document.write( " $\"abs%28x%2B6%29=2x\"$
\n" ); document.write( " $\"abs%286%2B6%29=2%2A6\"$
\n" ); document.write( " $\"12=12\"$
\n" ); document.write( "True statement.
\n" ); document.write( "Good answer.
\n" ); document.write( " $\"abs%28x%2B6%29=2x\"$
\n" ); document.write( " $\"abs%28-2%2B6%29=2%2A%28-2%29\"$
\n" ); document.write( " $\"abs%284%29=-4\"$
\n" ); document.write( " $\"4=-4\"$
\n" ); document.write( "False statement.
\n" ); document.write( "Not a good answer.
\n" ); document.write( "Here's why.
\n" ); document.write( "When we looked at the second solution,
\n" ); document.write( "we said \"When (x+6)<0\"
\n" ); document.write( " $\"%28x%2B6%29%3C0\"$
\n" ); document.write( " $\"x%3C-6\"$
\n" ); document.write( "We got an answer x=-2 which is not less than -6, so the answer is not valid.
\n" ); document.write( "There is only one solution.
\n" ); document.write( "x=6. \n" ); document.write( "

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