Question 85194: 2x-{4x-2[3x-4(2-2x)+6+4]-5x+3}
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given:
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2x-{4x-2[3x-4(2-2x)+6+4]-5x+3}
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A good approach is to start with the most interior set of parentheses and work your way
out from there. In this case the most interior set is the one that contains 2 - 2x.
Nothing can be done with the contents inside the parentheses, but you can do the distributed
multiplication by multiplying the -4 times each term inside the parentheses. When you do
that multiplication of -4 times (2 - 2x), the parentheses go away and your problem becomes:
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2x-{4x-2[3x-8+8x+6+4]-5x+3}
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Next look at the terms inside the brackets. These terms are:
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[3x-8+8x+6+4]
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and the like terms can be combined. Specifically you have 3x + 8x which add to 11x and
you have -8+6+4 which adds to +2. Therefore the terms inside the brackets are reduced to
11x + 2. Substitute [11x + 2] for the existing bracketed terms and the problem then is
simplified to:
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2x - {4x - 2[11x + 2]-5x + 3}
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Now do the distributed multiplication of -2 times the two terms inside the brackets.
The -2 times 11x gives you -22x and the -2 times the +2 gives you -4. The problem is
then simplified to:
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2x - {4x - 22x - 4 - 5x + 3}
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The like terms inside this set of brackets can also be combined. 4x - 22x - 5x algebraically
add up to -23x and the -4 and +3 add to -1. So the terms inside the brackets can be replaced
by -23x - 1 and the problem becomes:
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2x - {-23x - 1}
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Then since this set of brackets is preceded by the - sign, you can remove the brackets
if you change the sign of each term in the brackets. When you do that the simplified
version of the problem is now:
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2x + 23x + 1
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Combine the two x terms and the final answer is:
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25x + 1
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Hope this helps you to understand the process of how to work simplifications of this sort.
Not too hard, but you need to be careful not to make sign errors because it's easy to do.
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