Solving a two-step equation with integers

bobmane

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I am using aleks to get up to speed for college math. aleks does not always give the best explnations of what an actual rule is.
In this case, I understand that I use reverse order of operations and I know the steps. + or - then x or / depending on the problem.
The part that keeps getting me is only the "should I add or subtract" part (the very first step). the rest is easy.

I have looked around and all the examples I find just give one scenario and dont mention a rule pertaining to whether to + or - on that first step and why you would do one or the other.
 

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lev888

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Do you understand why we add or subtract? Once you get why this is done you won't need to remember any rules.
 

bobmane

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My understanding is we add or subtract to keep the balance. The reason step one involves performing one of those operations is because of the need to isolate x. So in removing by canceling on the one side we must balance the other.
 

lev888

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We do the same operation on both sides 'to keep the balance'. Yes, the reason to do in the first place is isolation of the variable or the term that includes the variable. To isolate the variable we need to remove everything else. So we add or subtract whatever is needed to cancel other terms.
 

bobmane

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I still dont understand how to choose + or - as first step.
 

lev888

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x + 2 = 5
How do we isolate x? We need to get rid of 2. So the first step is to subtract 2 on both sides since 2 - 2 = 0:
x + 2 - 2 = 5 - 2
x + 0 = 3
x = 3

x - 2 = 5
Now we want to get rid of (-2). How? By adding 2, since (-2) + 2 = 0.
 

bobmane

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Not clear your breakdown of those 2 cases addresses the various instances of the problem Like the ones I attached have various positive and negative numbers are not all quite as simple. Like -8 = -5 + 3u
If there are no negative numbers it is easier for sure.
 

lev888

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-8 = -5 + 3u
Based on the order of operations we isolate (solve for) 3u first, then solve for u.
How do we isolate 3u?
 

bobmane

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-5 - -5 = 0
 

lev888

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Ok, we subtract (-5) from both sides (which is the same as adding 5).
Can you finish solving it?
 

Subhotosh Khan

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-5 - -5 = 0
Great so you ADD 5 on both sides - because it will annihilate "-5".

-8 = -5 + 3u

-8 + 5 = -5 + 3u + 5

-3 = 3u

and continue....
 

bobmane

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"we subtract (-5) from both sides (which is the same as adding 5)"
you mean the same because it is a negative number but not the same if not a negative number?
 

lev888

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"we subtract (-5) from both sides (which is the same as adding 5)"
you mean the same because it is a negative number but not the same if not a negative number?
I mean subtracting -5 is equivalent to adding 5.
To simplify things just add 5 if you see -5 (don't subtract -5). The idea is to get 0. If there is -5 get rid of it with 5. And vice versa.
 

bobmane

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Thanks looks like the confusion was related to negative numbers (especially when there are several) more than anything else.
 
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