document.write( "Question 969763: Please help! I do not understand any of this!\r
\n" ); document.write( "\n" ); document.write( "Solve the following inequality 63x-32>63/x\r
\n" ); document.write( "\n" ); document.write( "a.) Is the point x=0 included in the solution set of the inequality?
\n" ); document.write( "b.) are the other finite end points of the interval included in the solution set?
\n" ); document.write( "c.) what is the solution set? (in interval notation) \n" ); document.write( "

Algebra.Com's Answer #592531 by Edwin McCravy(20060) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Although the other tutor got the right answer, she is incorrect\r\n" );
document.write( "for multiplying both sides of the inequality by the variable x.\r\n" );
document.write( "That's because a variable x might not be positive, and if you\r\n" );
document.write( "multiply through by a negative, that would reverse the > to <.\r\n" );
document.write( "Also she did not use test values on the intervals.  \r\n" );
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document.write( "Here is a correct solution:\r\n" );
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\n" ); document.write( "Solve the following inequality 63x-32>63/x
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document.write( "Get 0 on the right side by subtracting  from both sides:\r\n" );
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document.write( "Get the LCD = x on the left side:\r\n" );
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document.write( "Factor the numerator on the left:\r\n" );
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document.write( "We find all the critical numbers.  They are the values\r\n" );
document.write( "obtained by setting the numerator=0 and the denominator=0\r\n" );
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document.write( "The numerator (7x-9)(9x+7) when set equal to 0 gives \r\n" );
document.write( "critical numbers  and \r\n" );
document.write( "The denominator x when set equal to 0 gives the critical\r\n" );
document.write( "number 0.\r\n" );
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document.write( "We draw a number line and mark the critical numbers on it,\r\n" );
document.write( "in order from smallest to largest.\r\n" );
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document.write( "-----o------o--------------------o--------------\r\n" );
document.write( "   -7/9     0                   9/7    \r\n" );
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document.write( "We have 4 intervals to test by substituting a test point in the interval:\r\n" );
document.write( "1. Left of , which is \r\n" );
document.write( "2. Between  and , which is \r\n" );
document.write( "3. Between  and , which is \r\n" );
document.write( "4. Right of , which is \r\n" );
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document.write( "1. The easiest number in  to test in the original is x = -1\r\n" );
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document.write( "That's false so the solution set does not include \r\n" );
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document.write( "2. The easiest number in  to test in the original is x = -.1\r\n" );
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document.write( "That's true so the solution set does include \r\n" );
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document.write( "3. The easiest number in  to test in the original is x = 1\r\n" );
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document.write( "That's true so the solution set does include \r\n" );
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document.write( "3. The easiest number in  to test in the original is x = 2\r\n" );
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document.write( "That's true so the solution set does include \r\n" );
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document.write( "None of the critical numbers are part of the solution since the\r\n" );
document.write( "symbol is > and not ≥.\r\n" );
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document.write( "So the solution set is:\r\n" );
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\n" ); document.write( "a.) Is the point x=0 included in the solution set of the inequality?
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document.write( "No because if we substitute x=0,\r\n" );
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document.write( "It is meaningless to divide by zero.\r\n" );
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\n" ); document.write( "b.) are the other finite end points of the interval included in the solution set?
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document.write( "No because the symbol is > and not ≥\r\n" );
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\n" ); document.write( "c.) what is the solution set? (in interval notation)
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document.write( "Edwin

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