SOLUTION: is the absolute value equation always, sometimes, or never true? Explain 1) |x| = -6 2) |x| = x 3) |x|+|x| = 2x 4) |x+2| = x+2

Algebra ->  Absolute-value -> SOLUTION: is the absolute value equation always, sometimes, or never true? Explain 1) |x| = -6 2) |x| = x 3) |x|+|x| = 2x 4) |x+2| = x+2       Log On


   

Question 986213: is the absolute value equation always, sometimes, or never true? Explain
1) |x| = -6
2) |x| = x
3) |x|+|x| = 2x
4) |x+2| = x+2
Answer by ikleyn(52813) About Me  (Show Source):
You can put this solution on YOUR website!
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1) |x| = -6               Never true  (because the absolute value is always positive);

2) |x| = x               is true at x >= 0    (sometimes true:  infinitely many solutions.  But NOT always true:  is not true at  x < 0).

3) |x|+|x| = 2x       (2|x| = 2x; is true at x >= 0    I.e. sometimes true:  infinitely many solutions.  But NOT always true:  is not true at  x < 0).

4) |x+2| = x+2         (is true at x >= -2.  Is not true at x < -2.  Therefore,  sometimes true;  not always true).