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Question 72905: -4<-3x-13<26
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! -4<-3x-13<26
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Add 13 to all three sections of this inequality to get:
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-4 + 13 < -3x - 13 + 13 < 26 + 13
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This simplifies to
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+9 < -3x < 39
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Divide all three sections by -3 and you get:
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-3 < x < -13
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BUT a rule of inequalities is that if you multiply or divide by a negative number, the inequality
arrows flip around in the other direction. Don't forget this rule! And since we divided by
negative 3 we have to flip the arrows to get:
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-3 > x > -13
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This says that on the number line x lies between -3 and -13.
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Let's pick a number in this domain and substitute it into the original problem to make
sure that it works. -10 is an easy number to choose and it is between -3 and -13.
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The original problem was:
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-4<-3x-13<26
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Substituting -10 for x we get
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-4 < 30-13 < 26
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And solving the middle section results in:
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-4 < +17 < +26
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That's correct ... + 17 lies between -4 and + 26. That adds a little "comfort factor" that
our answer is correct.
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Hope this helps you to understand inequalities a little better.
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