Question 74333
You can work inequalities like these just as you would an equation with the exception that
if you divide or multiply both sides by a negative number, you need to reverse the direction of
the inequality sign.
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Let's treat this problem just like an equation that we would solve for q.
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7q - 1 + 2q < 29
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On the left side, combine the two terms by adding 7q and 2q to get:
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9q - 1 < 29
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Eliminate the -1 on the left side by adding +1 to both sides to get:
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9q < 30
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Now divide both sides by +9 in order to solve for q. This results in:
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q < (30/9)
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And dividing the both numerator and denominator by 3 reduces the fraction 30/9 to 10/3 
which is equivalent to "3 and 1/3"
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q < 10/3 
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The solution to this problem is that q can be any value smaller than 10/3. You can help
to convince yourself that this is correct by substituting for a couple values less than
10/3 and seeing that they make the inequality true. Then substitute for q a couple of 
numbers that are bigger than 10/3 and see that the equation is not true.
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Here's a couple of examples.  3 is less than 10/3. If we substitute 3 for q  in the original
problem the result is:
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(7*3) - 1 + (2*3) < 29
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which simplifies by multiplication to:
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21 - 1 + 6 < 29
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And by addition rules this reduces to:
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26 < 29
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Which is true.
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Now let's let q be 4 which is slightly greater than 10/3.  The original problem becomes:
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(7*4) - 1 + (2*4) < 29
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which simplifies by multiplication to:
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28 - 1 + 8 < 29
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And by addition rules this reduces to:
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35 < 29
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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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Notice that in this problem we did not have to multiply or divide both sides by a negative 
number so the direction of the inequality remains unchanged from its original direction.
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Hope this helps you to understand the properties of inequalities a little better.