combining like terms - error in my pattern: 25 - (-10m) + 7 + 5m - (-3) + 26 = ?

[steveopolis]

Overall, I have "combining like terms" down. However, in my math class, I keep getting ones like this wrong:

25 - (-10m) + 7 + 5m - (-3) + 26 =

It seems to be an error around my idea of having "used up" the "-" sign. In this example, I am unsure whether to go:

25 + 7 - (-3) + 26 + [-(-10) + 5m], i.e. 61 + 15m
OR
[25 + 7 - (-3) + 26] - [(-10) + 5m], i.e. 61 - (-5m)

 

[tkhunny]

Overall, I have "combining like terms" down. However, in my math class, I keep getting ones like this wrong:

25 - (-10m) + 7 + 5m - (-3) + 26 =

It seems to be an error around my idea of having "used up" the "-" sign. In this example, I am unsure whether to go:

25 + 7 - (-3) + 26 + [-(-10) + 5m], i.e. 61 + 15m
OR
[25 + 7 - (-3) + 26] - [(-10) + 5m], i.e. 61 - (-5m)

Sorry, they're both a little off.

First, I would NEVER tolerate all those negative signs. Resolve them FIRST. Far too confusing with all that in there.

25 - (-10m) + 7 + 5m - (-3) + 26

25 + 10m + 7 + 5m + 3 + 26

Now collect

25 + 7 + 3 + 26 + m(10 + 5) -- No confusion necessary.

Also, when you collected -(-10m) + 5m, you managed to get [-(-10) + 5m]. That's no good. The m is no longer attached to the 10. You obviously didn't actually mean that, since you added the 10 and the 5 to get 15m, but what you have written doesn't mean that. It would have been okay with the right square bracket in a different place, namely [-(-10) + 5]m

 

[steveopolis]

Thank you, tkhunny!

Yes, I accidentally omitted that m.

Your system is nice and clean. I'm going to try a bunch using that way and see if that helps eliminate the points of my confusion. I think it will

 

[Steven G]

Overall, I have "combining like terms" down. However, in my math class, I keep getting ones like this wrong:

25 - (-10m) + 7 + 5m - (-3) + 26 =

It seems to be an error around my idea of having "used up" the "-" sign. In this example, I am unsure whether to go:

25 + 7 - (-3) + 26 + [-(-10) + 5m], i.e. 61 + 15m
OR
[25 + 7 - (-3) + 26] - [(-10) + 5m], i.e. 61 - (-5m)

tkhunny is absolutely correct about getting rid of some of the negative signs! Having said that I will answer your question (but in the future get rid of the negative signs!).

You have -(-10m) + 5m. Now that red -sign is only for the (-10m) and NOT for the + 5m. So to combine them you have [-(-10) + 5]m = [10 + 5]m = 15m

It would be much easier to say -(-10m) + 5m = 10m + 5m = 15m from the start

 

[steveopolis]

Thanks, Jomo