document.write( "Question 1148045: If x is twice as far from -9 as it is from 3,what are the possible values of x? \n" ); document.write( "

Algebra.Com's Answer #769465 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " It can be solved algebraically, but a geometric solution is more impressive -- so, I will show you it . . . \r
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document.write( "a)  On the number line, \"x\" is to the left from -9.\r\n" );
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document.write( "        Then it is clear that THERE IS NO solution in this case.\r\n" );
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document.write( "         (It is OBVIOUS, so I will not try to prove it).\r\n" );
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document.write( "b)  On the number line, \"x\" is between  -9 and 3.\r\n" );
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document.write( "        Then the distance from -9 to 3 is 12 units, and we should divide it in proportion 2:1, counting from left to right.\r\n" );
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document.write( "        Obviously, the point x= -1 divide the segment [-12,3] in this proportion.\r\n" );
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document.write( "        So, x= -1 is the solution in this case.\r\n" );
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document.write( "c)  On the number line, \"x\" is to the right from 3.\r\n" );
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document.write( "        Again, recall that the distance from -9 to 3 is 12 units;\r\n" );
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document.write( "        so, we need move 12 units to the right from 3; then we get x= 3+12 = 15.\r\n" );
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document.write( "        Thus x= 15 is the solution in this case.\r\n" );
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document.write( "ANSWER.  The problem has two solutions:  x= -1  and  x= 15.\r\n" );
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