document.write( "Question 999927: If |x|+|x-1|=3 then x=? \n" ); document.write( "
Algebra.Com's Answer #617458 by ikleyn(52781)\"\" \"About 
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document.write( "Answer. This equation has two solutions: x = 2 and x = -1.\r\n" );
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document.write( "Solution\r\n" );
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document.write( "1.  If x < 0, then |x| = -x and |x-1| = -(x-1), therefore |x| + |x-1| = -x -(x-1) = -2x + 1. \r\n" );
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document.write( "    Hence,  the equation |x| + |x-1| = 3 takes the form -2x + 1 = 3.\r\n" );
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document.write( "    The last equation has the solution x = -1,  which satisfies the inequality x < 0.\r\n" );
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document.write( "2.  If 0 <= x < 1, then |x| = x and |x-1| = -(x-1), therefore |x| + |x-1| = x -(x-1) = 1. \r\n" );
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document.write( "    Hence,  the equation |x| + |x-1| = 3 takes the form 1 = 3.\r\n" );
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document.write( "    The last equation has no solution.\r\n" );
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document.write( "3.  If x >= 1, then |x| = x and |x-1| = (x-1), therefore |x| + |x-1| = x + (x-1) = 2x - 1. \r\n" );
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document.write( "    Hence,  the equation |x| + |x-1| = 3 takes the form 2x - 1 = 3.\r\n" );
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document.write( "    The last equation has the solution x = 2,  which satisfies the inequality x >= 1.\r\n" );
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document.write( "The plot of the function y = |x| + |x-1| is presented in the Figure below.\r\n" );
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document.write( "      Figure. Plot y = |x| + |x-1|\r\n" );
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