document.write( "Question 986213: is the absolute value equation always, sometimes, or never true? Explain
\n" ); document.write( "1) |x| = -6
\n" ); document.write( "2) |x| = x
\n" ); document.write( "3) |x|+|x| = 2x
\n" ); document.write( "4) |x+2| = x+2
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #607026 by ikleyn(52814)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "1) |x| = -6               Never true  (because the absolute value is always positive);\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2) |x| = x               is true at x >= 0    (sometimes true:  infinitely many solutions.  But NOT always true:  is not true at  x < 0). \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "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).\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "4) |x+2| = x+2         (is true at x >= -2.  Is not true at x < -2.  Therefore,  sometimes true;  not always true). \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );