SOLUTION: I'm taking a elementary and intermediate algebra in college. It's been a very long while since I have done algebra. I'm trying to figure out where do I start first within this expr

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Question 100887: I'm taking a elementary and intermediate algebra in college. It's been a very long while since I have done algebra. I'm trying to figure out where do I start first within this expression
[3-(2-4)][3+|2-4|]
also
8-3|5-4 2ndpower + 1|
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
First problem. Given:
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[3-(2-4)][3+|2-4|]
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We can start by working this in two parts. [3-(2-4)] is one part and [3+|2-4|] is the other.
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For the part [3-(2-4)] start with the "nested" or interior set of parentheses. In those
parentheses you have (2-4) and when you combine those two numbers, the result is (-2). Therefore,
you can substitute (-2) with its parentheses and you get [3-(-2)]. Since the parentheses
are preceded by a minus sign you can remove them if you change the sign of the number inside
the parentheses. (You can also look at this as a multiplication of the number inside the
parentheses by a minus 1.) When you remove the parentheses you get [3 + 2] and this simplifies
to [5]. So the first part is just [5]
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Next work the second part which is [3+|2-4|]. I assume that the "|" and "|" enclosures are
the standard notation meaning absolute value. The absolute value symbols mean that anything
inside them will come outside as a positive value. So let's start with the "nested" or
interior set of absolute value signs which are |2-4|. Combine the two interior numbers and
you get |-2|. But the absolute value of |-2| = (+2) by the definition of absolute value. Making
this substitution in two steps you get [3+ (+2)] and since the parentheses are preceded by
a plus sign, they can be removed without changing the sign of their contents to get just
[3 + 2]. Simplify this by just adding the two numbers to get [5]. This means that
[3+|2-4|] is equal to [5].
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So now we have reduced the two parts of the original problem and we substitute the equivalent
values for [3-(2-4)][3+|2-4|] to get [5][5] and this multiplication results in the answer
for this problem being 25.
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Onward to the second problem:
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I hope that I interpreted correctly what you wrote. Start inside the absolute value signs.
First, let's square the 4 to get 16. [Notice that you interpret this as
and not as .] When you substitute this into the problem you have:
.

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Now combine the three numbers inside the absolute value signs. 5-16+1 combine to -10. Substitute
this into the problem and you have:
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but recall the definition of absolute value. The absolute value of -10 is +10, so you can
replace by and the problem becomes:
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Now you do the multiplication of -3 times 10 to get -30 and with that substitution
the problem becomes and these two numbers combine to give . So the answer
to this problem is .
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As a final note, the general order of algebraic manipulations is:
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1. Do things in parentheses or other grouping symbols first, working from the interior sets outward
2. Do the exponential terms
3. From left to right do the multiplications and divisions as you encounter them.
4. From left to right do the additions and subtractions as you encounter them
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Takes a lot of practice before you get the hang of doing these things ... so hang tough.
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Hope I correctly interpreted the way you wrote these two problems and I hope this helps you
to understand the concept of working your way from the inside set of parentheses or "groupings"
to the outside set.
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