document.write( "Question 152651: how many solutions are there to |x+2| = 14
\n" ); document.write( "a. 1
\n" ); document.write( "b. 2
\n" ); document.write( "c. -16
\n" ); document.write( "d. none of the above \n" ); document.write( "

Algebra.Com's Answer #112285 by mducky2(62) $\"\"$ $\"About$

You can put this solution on YOUR website!
We could solve this easily just by solving for x. In order to solve an absolute value equation, we usually have to divide it up into two parts, since the expression $\"x+%2B+2\"$ is either positive or negative.
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If we assume it's positive, then the absolute value signs don't even matter. We can just remove them and solve:
\n" ); document.write( " $\"x+%2B+2+=+14\"$
\n" ); document.write( " $\"x+%2B+2+-+2+=+14+-+2+\"$
\n" ); document.write( " $\"x+=+12\"$
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Now let's assume $\"x+%2B+2\"$ is negative. If it were, then the absolute value sign changed it to be positive. The only way we can do that without absolute value signs is to multiply $\"x+%2B+2\"$ times -1. Then we can solve it:
\n" ); document.write( " $\"%28-1%29%28x%2B2%29+=+14\"$
\n" ); document.write( " $\"-x+-+2=+14\"$
\n" ); document.write( " $\"-x+-+2+%2B+2+=+14+%2B+2\"$
\n" ); document.write( " $\"-x+=+16\"$
\n" ); document.write( " $\"%28-1%29%28-x%29+=+%28-1%29%2816%29\"$
\n" ); document.write( " $\"x+=+16\"$
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Since we've found all the solutions to x, whether $\"x%2B2\"$ is positive or negative, we know that there are 2 solutions to $\"abs%28x%2B2%29=+14\"$ . \n" ); document.write( "

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