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
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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(52814) (Show Source): You can put this solution on YOUR website!
.
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).
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