document.write( "Question 1177686: Solve|x²-9|>7
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Algebra.Com's Answer #806787 by ikleyn(53765) $\"\"$ $\"About$

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document.write( "1)  From one side, if  x^2 - 9 >= 0,  i.e.  {x <= -3  OR  x >= 3},\r\n" );
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document.write( "    then  |x^2 - 9| = x^2 - 9 > 7,  x^2 > 7+9 = 16,  which implies  (x < -4} OR {x > 4}.\r\n" );
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document.write( "        So, one set of solution is  (-oo,-4) U (4,oo).\r\n" );
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document.write( "2)  From the other side, if  x^2 - 9 < 0,  i.e.  {-3 < x < 3},\r\n" );
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document.write( "    then  |x^2 - 9| = 9-x^2 > 7,  9 - 7 > x^2,  x^2 < 2,  which implies  -sqrt(2) < x < sqrt(2).\r\n" );
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document.write( "        So, the other set of solution is   < x < .\r\n" );
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document.write( "3)  Finally, the solution set is the union of three intervals\r\n" );
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document.write( "        (-oo,-4) U ( ,  ) U (4,oo).\r\n" );
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document.write( "4)  Visually, the solution set is seen and confirmed from this plot\r\n" );
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document.write( "    \r\n" );
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document.write( "       Plot  y = |x^2 - 9|  (red)  and  y = 7  (green)\r\n" );
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document.write( "The solution set is where the red line is ABOVE the green line.\r\n" );
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