SOLUTION: Is the equation √[ (3x +7)2] = 3x + 7 sometimes true, always true, or never true? Help? Can someone explain this to me? Thank you. Cynthia

Algebra ->  Absolute-value -> SOLUTION: Is the equation √[ (3x +7)2] = 3x + 7 sometimes true, always true, or never true? Help? Can someone explain this to me? Thank you. Cynthia      Log On


   

Question 286513: Is the equation √[ (3x +7)2] = 3x + 7 sometimes true, always true, or never true?
Help? Can someone explain this to me?
Thank you.
Cynthia
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28%283x%2B7%29%5E2%29=3x%2B7 is only true if %283x%2B7%29%3E=0 since sqrt%28%283x%2B7%29%5E2%29=abs%283x%2B7%29 for all values of 'x'. So the answer is 'sometimes true'.

Here are some examples: If x=0, then sqrt%28%283%280%29%2B7%29%5E2%29=3%280%29%2B7 ---> sqrt%287%5E2%29=7 ----> 7=7 which is true.

However, If x=-10, then sqrt%28%283%28-10%29%2B7%29%5E2%29=3%28-10%29%2B7 ---> sqrt%28%28-28%29%5E2%29=-28 ----> 28=-28 which is false.