Keeyn

New member
Hey guys, I have a question to ask. You know how we can break down 8(5) in a simple expression such as 3-8(5) to solve 8(5) first right? So I have another question. In a simple expression like (2x+5)+2, can we look at 2x+5 separately first which still gives 2x+5 or we need to see (2x+5)+2 as the bare minimum to give 2x+5+2? Arghhhhhh this question is bugging me. I used to break down (2x+5)+2 until I thought why not ignore the +2 first like how we ignore the 3 in 3-8(5) to calculate what we have first to make it simpler? Do you guys understand what I am asking? Erm...even though there is nothing to solve about 2x+5...I mean, can we look at it separately from the expression FIRST or the bare minimum to break down the expression is still (2x+5)+2? Please help.

Dr.Peterson

Elite Member
Hey guys, I have a question to ask. You know how we can break down 8(5) in a simple expression such as 3-8(5) to solve 8(5) first right? So I have another question. In a simple expression like (2x+5)+2, can we look at 2x+5 separately first which still gives 2x+5 or we need to see (2x+5)+2 as the bare minimum to give 2x+5+2? Arghhhhhh this question is bugging me. I used to break down (2x+5)+2 until I thought why not ignore the +2 first like how we ignore the 3 in 3-8(5) to calculate what we have first to make it simpler? Do you guys understand what I am asking? Erm...even though there is nothing to solve about 2x+5...I mean, can we look at it separately from the expression FIRST or the bare minimum to break down the expression is still (2x+5)+2? Please help.
It's not easy to follow what you are saying; your term "break down" is confusing, and you are using "solve" where you mean "evaluate".

I think you are saying that when you are evaluating the expression 3 - 8(5), you do the multiplication 8(5) = 40 first, and then evaluate 3 - 40 = -37. This is a matter of determining the meaning of the expression, following the traditional order of operations; sometimes there can be other ways you can carry out an evaluation, which are guaranteed to give the same result.

All you can do with the expression (2x + 5) + 2 is to simplify it. Here, the parentheses have no real effect (because we normally evaluate left to right anyway), so we can write it as 2x + 5 + 2; but more important, we can apply the associative property of addition to see that it is equivalent to 2x + (5 + 2) = 2x + 7.

If you were evaluating the expression for some given value of x, then you would, as you suggest, evaluate 2x + 5 first, then add 2. Or, you could use the facts I mentioned in the last paragraph, and just evaluate 2x + 7. You will get the same result either way.

Keeyn

New member
I don’t know, I mean...I always do maths in such a way that I take parts of the expression and evaluate it (following the bodmas rule of course). But when I do, I make sure that what I am evaluating at one time is to the ‘’most basic’’ already. Because, when the expression gets complicated, we will look at its smaller counterparts first whether or not we realise that we are doing it. For example, to me, if I were to evaluate the expression 6+(2x+5)+5(3) for example, I would do +(2x+5) to give +2x+5 and then after doing this, I will move on to +(5)(3) to give a +15, although I am not sure this is right...instead of just evaluating 6+(2x+5)+5(3) to give 6+2x+5+15 straight. Another example would be, 5*(6+2x+2x), I would do +2x+2x to give a +4x first, instead of like taking 6+2x+2x as a whole to give 6+4x, because like I said I would evaluate it down to the ‘most basic’ and for 6+2x+2x, I could still ignore the 6 and do +2x+2x first. So what I wanted to know in my first post is, whether something like (2x+5)+2 we have to see it as (2x+5)+2 as a whole because I cannot ‘break down’ the expression into smaller counterparts, or I can look at 2x+5 individually first (even though there is nothing to evaluate about 2x+5), so it still gives 2x+5 and then followed by a +2? Sorry for the confusing post, even I am confused myself.

mmm4444bot

Super Moderator
Staff member
… In a simple expression like (2x+5)+2, can we look at 2x+5 separately first which still gives 2x+5 or we need to see (2x+5)+2 as the bare minimum to give 2x+5+2?
If you're looking at the expression:

(2x + 5) + 2

and you're seeing this part as a separate object than this part, that's good! The "main point" of this expression (if I may refer to it as such) is that two objects are being summed (added), as indicated by the bold plus sign.

So, it's not necessary to view the given expression as 2x + 5 + 2, at the start. What's important here is the process of simplification -- and that concept has to do with "combining like-terms".

Therefore, after you see 2x+5 as one object, and then parse (break down?) that a second object is being added to the first, your next thought is to recognize that 5 and 2 are like-terms (i.e., they are both constants) -- different from 2x (which is a variable term). In other words, we simplify the given expression by combining the like-terms:

2x + 7

Also, be aware that there are often a number of ways to carry out steps that all arrive at the same result. So, a personal style eventually takes hold.

If you're thinking about something else (regarding break downs and bare minimums), please explain in more detail. Thanks

Keeyn

New member
Simply put, you guys know how I can break open the bracket when it comes to (2x+5), but cannot when it comes to the 2x+5 in (2x+5)(3x+4) right? So in (2x+5)+2, can I look at 2x+5 to break open the bracket? Or does the expression becomes 2x+5+2 because we have to look at (2x+5)+2 as a whole? Thanks, Ang help will be appreciated.

Dr.Peterson

Elite Member
I don’t know, I mean...I always do maths in such a way that I take parts of the expression and evaluate it (following the bodmas rule of course). But when I do, I make sure that what I am evaluating at one time is to the ‘’most basic’’ already. Because, when the expression gets complicated, we will look at its smaller counterparts first whether or not we realise that we are doing it. For example, to me, if I were to evaluate the expression 6+(2x+5)+5(3) for example, I would do +(2x+5) to give +2x+5 and then after doing this, I will move on to +(5)(3) to give a +15, although I am not sure this is right...instead of just evaluating 6+(2x+5)+5(3) to give 6+2x+5+15 straight. Another example would be, 5*(6+2x+2x), I would do +2x+2x to give a +4x first, instead of like taking 6+2x+2x as a whole to give 6+4x, because like I said I would evaluate it down to the ‘most basic’ and for 6+2x+2x, I could still ignore the 6 and do +2x+2x first. So what I wanted to know in my first post is, whether something like (2x+5)+2 we have to see it as (2x+5)+2 as a whole because I cannot ‘break down’ the expression into smaller counterparts, or I can look at 2x+5 individually first (even though there is nothing to evaluate about 2x+5), so it still gives 2x+5 and then followed by a +2? Sorry for the confusing post, even I am confused myself.
When I asked what your goal was, I was asking what you are trying to do with the expression.

If you are told to evaluate it for some value of x, then you can do whatever you do in evaluating any expression, piece by piece. If x = 4, then 2x is 8; 2x + 5 is 13; and (2x + 5) + 2 is 15.

If you are told to simplify the expression, then you do what I suggested using the associative property. Are you familiar with that? Have you learned to simplify expressions yet?

The expression certainly is a whole; but I don't see why you say you "can't break it down". It does consist of (2x + 5) and 2, which are added together.

Dr.Peterson

Elite Member
Simply put, you guys know how I can break open the bracket when it comes to (2x+5), but cannot when it comes to the 2x+5 in (2x+5)(3x+4) right? So in (2x+5)+2, can I look at 2x+5 to break open the bracket? Or does the expression becomes 2x+5+2 because we have to look at (2x+5)+2 as a whole? Thanks, Ang help will be appreciated.
What does "break open the bracket" mean? Is that something you've been taught, or your own terminology?

The reason you can rewrite (2x+5)+2 as 2x+5+2 is simply that they mean the same thing: to evaluate either, you would add 2x and 5, then add 2 -- in the first case because the parentheses tell you to do that first, and in the second, because we evaluate left to right.

In other cases, like 2(2x + 5) = 4x + 10, you can do it because there is a property (in this case, the distributive property) that tells you that doing this doesn't change the value of the expression.

The reason you can't rewrite (2x+5)(3x+4) as 2x+5(3x+4), if that's what you mean, is that they don't mean the same thing. There is no rule that says they are the same, so you can't do that.

All you have to do is know what you can do, and only do that! It's not about having to look at something as a whole; it's about knowing what changes to the parts leave the value unchanged.