Question 74333This question is from textbook
: solve the inequality
7q-1+2q<29
This question is from textbook
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 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.
.
Hope this helps you to understand the properties of inequalities a little better.
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