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You can put this solution on YOUR website!
You can work inequalities like these just as you would an equation with the exception that
\n" ); document.write( "if you divide or multiply both sides by a negative number, you need to reverse the direction of
\n" ); document.write( "the inequality sign.
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\n" ); document.write( "Let's treat this problem just like an equation that we would solve for q.
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\n" ); document.write( "7q - 1 + 2q < 29
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\n" ); document.write( "On the left side, combine the two terms by adding 7q and 2q to get:
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\n" ); document.write( "9q - 1 < 29
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\n" ); document.write( "Eliminate the -1 on the left side by adding +1 to both sides to get:
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\n" ); document.write( "9q < 30
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\n" ); document.write( "Now divide both sides by +9 in order to solve for q. This results in:
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\n" ); document.write( "q < (30/9)
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\n" ); document.write( "And dividing the both numerator and denominator by 3 reduces the fraction 30/9 to 10/3
\n" ); document.write( "which is equivalent to \"3 and 1/3\"
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\n" ); document.write( "q < 10/3
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\n" ); document.write( "The solution to this problem is that q can be any value smaller than 10/3. You can help
\n" ); document.write( "to convince yourself that this is correct by substituting for a couple values less than
\n" ); document.write( "10/3 and seeing that they make the inequality true. Then substitute for q a couple of
\n" ); document.write( "numbers that are bigger than 10/3 and see that the equation is not true.
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\n" ); document.write( "Here's a couple of examples. 3 is less than 10/3. If we substitute 3 for q in the original
\n" ); document.write( "problem the result is:
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\n" ); document.write( "(7*3) - 1 + (2*3) < 29
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\n" ); document.write( "which simplifies by multiplication to:
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\n" ); document.write( "21 - 1 + 6 < 29
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\n" ); document.write( "And by addition rules this reduces to:
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\n" ); document.write( "26 < 29
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\n" ); document.write( "Which is true.
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\n" ); document.write( "Now let's let q be 4 which is slightly greater than 10/3. The original problem becomes:
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\n" ); document.write( "(7*4) - 1 + (2*4) < 29
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\n" ); document.write( "which simplifies by multiplication to:
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\n" ); document.write( "28 - 1 + 8 < 29
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\n" ); document.write( "And by addition rules this reduces to:
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\n" ); document.write( "35 < 29
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\n" ); document.write( "And this is not true. In this case when q is greater than 10/3 it won't make the inequality true.
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\n" ); document.write( "Notice that in this problem we did not have to multiply or divide both sides by a negative
\n" ); document.write( "number so the direction of the inequality remains unchanged from its original direction.
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\n" ); document.write( "Hope this helps you to understand the properties of inequalities a little better. \n" ); document.write( "