document.write( "Question 1010355: Find the solution set (algebraically) to the inequality below:
\n" ); document.write( "√(x+7)+5 < x \n" ); document.write( "
Algebra.Com's Answer #625799 by Edwin McCravy(20055) $\"\"$ $\"About$
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document.write( "What's under the square root radical cannot be negative,\r\n" );
document.write( "so we have a critical number when x+7=0 or x=7.\r\n" );
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document.write( "First we solve the equation of the boundary \r\n" );
document.write( "to find all other potential critical numbers besides -7.\r\n" );
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document.write( "Isolate the square root term on the left:\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "From that we get critical values 2 and 9\r\n" );
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document.write( "We put all three critical values on a number line\r\n" );
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document.write( "-------o--------------------------o--------------------o------\r\n" );
document.write( "-9 -8 -7 -6 -5 -4 -3 -2 -1  0  1  2  3  4  5  6  7  8  9 10 11\r\n" );
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document.write( "So we test the original inequality in each of the intervals \r\n" );
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document.write( "Testing the inequality \r\n" );
document.write( "Choose test value -8 and substitute in the original inequality:\r\n" );
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document.write( "That's not a real number on the left, so we do not use that \r\n" );
document.write( "interval.\r\n" );
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document.write( "Testing the inequality \r\n" );
document.write( "Choose test value 0 and substitute in the original inequality:\r\n" );
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document.write( "That's false, so we do not use that interval.\r\n" );
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document.write( "Testing the inequality \r\n" );
document.write( "Choose test value 3 and substitute in the original inequality:\r\n" );
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document.write( "That's false, so we do not use that interval.\r\n" );
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document.write( "Testing the inequality \r\n" );
document.write( "Choose test value 10 and substitute in the original inequality:\r\n" );
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document.write( "That's true, so we use that interval \r\n" );
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document.write( "Now we test the critical values themselves:\r\n" );
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document.write( "Testing critical value -7\r\n" );
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document.write( "That's false.\r\n" );
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document.write( "Testing critical value 2\r\n" );
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document.write( "That's false.\r\n" );
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document.write( "Testing critical value 9\r\n" );
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document.write( "That's false. So the interval is open at 9\r\n" );
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document.write( "Answer: \r\n" );
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document.write( "Edwin
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