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Question 70627: I need to solve the following inequalities and show on a real number line.
5x-2>2(1+3x)-x
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! 5x-2 > 2(1+3x)-x
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This is a "Trick" Problem
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You can begin by treating this just like an equation as far as the math is concerned.
First do the multiplication on the right side. Multiply 2 times (1+3x). When you do that the
problem becomes:
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5x - 2 > 2 + 6x - x
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Next combine the 6x and -x on the right side. The inequality becomes:
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5x - 2 > 2 + 5x
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To get rid of the -2 on the left side, add +2 to both sides. The inequality is then
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5x > 4 + 5x
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You may see the problem at this point. How can you add +4 to something (on the right side)
and have it be less than the something without the 4 (left side)? But let's continue.
To eliminate the 5x on the right side, add -5x to both sides. The inequality then becomes:
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0 > 4
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That sure isn't true. This tells you that there is NO value of x that will make the original
inequality true. The original inequality has been reduced to something that can never be
true. Don't mark any regions on the number line.
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Somebody was trying to sneak this problem by you. It probably made you think about
inequalities, though, and that may have been the purpose of the exercise ... just to
get you to think.
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