document.write( "Question 1121927: How do you write an absolute value equation that has the solutions x=−10
\n" ); document.write( " and x=−5? \n" ); document.write( "

Algebra.Com's Answer #737942 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "Use the idea that
\n" ); document.write( " $\"abs%28x-a%29=b\"$
\n" ); document.write( "means b is the distance between x and a.

\n" ); document.write( "In your example, the values x=-10 and x=-5 are each a distance of 2.5 from x = -7.5. So the absolute value equation you want is the one that says the distance between x and -7.5 is 2.5.

\n" ); document.write( "Use the pattern to insert the numbers in your example.

\n" ); document.write( "If you don't quite understand yet, here is another example.

\n" ); document.write( "Suppose we want the two solutions to be -10 and 34.

\n" ); document.write( "The point midway between -10 and 34 is ((-10+34)/2) = 12; the distance between 12 and either -10 or 34 is 22.

\n" ); document.write( "So the absolute value equation has to say that the distance between x and 12 is 22. Plugging those numbers into the pattern gives us the answer:

\n" ); document.write( " $\"abs%28x-12%29=22\"$ \n" ); document.write( "

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