document.write( "Question 653235: find the solution to the inequality : x² ≧ 25
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Algebra.Com's Answer #408312 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "               x² ≧ 25\r\n" );
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document.write( "Get 0 on the right side:\r\n" );
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document.write( "          x² - 25 ≧ 0\r\n" );
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document.write( "Get the critical numberss by solving the\r\n" );
document.write( "equation gotten by changing the inequality\r\n" );
document.write( "symbol to 0.\r\n" );
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document.write( "          x² - 25 = 0\r\n" );
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document.write( "   (x - 5)(x + 5) = 0\r\n" );
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document.write( "x - 5 = 0;  x + 5 = 0\r\n" );
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document.write( "    x = 5;      x = -5\r\n" );
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document.write( "Place the critical values on a number line:\r\n" );
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document.write( "--------o---------o---------\r\n" );
document.write( "       -5         5\r\n" );
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document.write( "Pick a test value to the left of -5, say -6\r\n" );
document.write( "Substitute -6 into the inequality\r\n" );
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document.write( "   x² - 25 ≧ 0\r\n" );
document.write( "(-6)² - 25 ≧ 0\r\n" );
document.write( "   36 - 25 ≧ 0\r\n" );
document.write( "        11 ≧ 0\r\n" );
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document.write( "That is true so we shade the region of\r\n" );
document.write( "the number line to the left of -5\r\n" );
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document.write( "<=======o---------o---------\r\n" );
document.write( "       -5         5\r\n" );
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document.write( "Now pick a test value between -5 and 5, say 0.\r\n" );
document.write( "Substitute 0 into the inequality\r\n" );
document.write( "  x² - 25 ≧ 0\r\n" );
document.write( "(0)² - 25 ≧ 0\r\n" );
document.write( "   0 - 25 ≧ 0\r\n" );
document.write( "      -25 ≧ 0\r\n" );
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document.write( "That is false so we DO NOT shade the region\r\n" );
document.write( "of the number line between -5 and 5. So we\r\n" );
document.write( "still have:\r\n" );
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document.write( "<=======o---------o---------\r\n" );
document.write( "       -5         5\r\n" );
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document.write( "Pick a test value to the right of 5, say 6\r\n" );
document.write( "Substitute 6 into the inequality\r\n" );
document.write( "  x² - 25 ≧ 0\r\n" );
document.write( "(6)² - 25 ≧ 0\r\n" );
document.write( "  36 - 25 ≧ 0\r\n" );
document.write( "       11 ≧ 0\r\n" );
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document.write( "That is true so we shade the region of\r\n" );
document.write( "the number line to the right of 5\r\n" );
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document.write( "<=======o---------o========>\r\n" );
document.write( "       -5         5\r\n" );
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document.write( "Now we test the critical points themselves:\r\n" );
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document.write( "Testing -5:\r\n" );
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document.write( "   x² - 25 ≧ 0\r\n" );
document.write( "(-5)² - 25 ≧ 0\r\n" );
document.write( "   25 - 25 ≧ 0\r\n" );
document.write( "         0 ≧ 0\r\n" );
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document.write( "That's true, so we darken the circle at -5\r\n" );
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document.write( "<=======⚫--------o========>\r\n" );
document.write( "       -5         5\r\n" );
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document.write( "Testing 5:\r\n" );
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document.write( "  x² - 25 ≧ 0\r\n" );
document.write( "(5)² - 25 ≧ 0\r\n" );
document.write( "  25 - 25 ≧ 0\r\n" );
document.write( "        0 ≧ 0\r\n" );
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document.write( "That's true, so we darken the circle at 5\r\n" );
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document.write( "<=======⚫--------⚫========>\r\n" );
document.write( "       -5         5\r\n" );
document.write( "The interval notation is an abbreviation\r\n" );
document.write( "of that graph.\r\n" );
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document.write( "     (-∞,-5] U [5,∞)  \r\n" );
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document.write( "Edwin
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