##### When solving an absolute value equation, |x + n| = c (where c&gt; 0

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When solving an absolute value equation, |x + n| = c (where c> 0), either the expression inside the absolute value is equal to c or the opposite of the expression is equal to c. Is this true or false?

Jun 26th, 2015

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|x + n| = c   , c> 0

implies

x + n =c or  -(x + n) = c

So, it is true that expression inside the absolute value is equal to c or the opposite of the expression is equal to c.

For example,

Let n= 2 and c = 5

So,

|x + 2| = 5  implies

x+ 2 = 5   or -(x + 2) = 5

x = 5 - 2   or  -x - 2 = 5

x = 3        or  -x = 5 + 2

x = 3        or  -x = 7

x = 3        or   x = -7

So, if x = 3 => |3 + 2| = |5| = 5

If x = -7 => |-7 + 2| = |-5| = 5

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Jun 26th, 2015

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Jun 26th, 2015
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Jun 26th, 2015
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