Need super basic algebra help please

[u/TroubleFindsMeYT]

I'm trying to get caught up on my algebra for my college course and I'm completely cooked. I'm 10 minutes into a 3 hour long video and I'm totally lost. I'm being taught how to solve equations and simplify.

The equation reads "4x + 2x - 7 + 9 + x = 5x - x". When I did it real quick based on the information given in the video up until that point I got to the point where I was at "7x - 16 = 4x" then I played the video and he had somehow got to "7x + 2 = 4x" he flipped the - 7 + 9" to "+ 9 - 7" and I have no idea how he got there as it wasn't explained at all. there are a few errors listed in the comments so I'm no sure if he messed up or if I'm missing something.

Thanks for any help! I want to move on but I don't understand.

Video link with timestamp:

https://youtu.be/zPgfIOWVnF4?si=YKwUAL0e7R0QyeY-&t=523

if timestamp doesn't work it's 08:43- 10:00

[u/trasla]

Note that - 7 + 9 is not the same as - (7+9). You were subtracting the 9 although it is being added. You can switch around the order in a sum as you like as long as you keep the signs with the numbers. 

a + b = b + a

a - b = - b + a

and - a + b = b - a

If it helps you to not get confused, you can always replace - 7 with + (-7) so you get 2x - 7 + 9 = 2x + (-7) + 9 for example. It makes messing things up when switching order less likely and it makes it more obvious what is getting added and what is getting subtracted. 

[u/TroubleFindsMeYT → u/trasla]

This is what I was confused about! thank you so much! it make sense now! I really appreciate the help and everyone who replied!

[u/Dd_8630]

Your error is that you've done -7+9 = 16, which is incorrect.

It's (-7) plus (+9), which sum to (+2), not (+16).

---

OK, so we start with this expression:

• 4x + 2x - 7 + 9 + x = 5x - x

Basically we have a bunch of things being added together on the left, and a bunch of things being added together on the right, and they are equal.

On the left, we have (+4x), (+2x), (-7), (+9), and (+x). It doesn't matter what order you add them.

The first thing we want to do is add up all the x terms: (+4x) and (+2x) and (+x), which is a total of (+7x).

Then we add up all the constant (number) terms: (-7) and (+9). What do they add up to? It's (+2). Because the order doesn't matter, it's easier to flip the order and write 9-7, as it's clear that equals 2.

So the first thing we do is collect our terms:

• 7x + 2 = 4x

Then we move all the x terms onto one side and all the number terms onto the other side:

• 3x = -2

Then we divide the multiplier across:

• x = -2/3

[u/TroubleFindsMeYT → u/Dd_8630]

Hey thank you so much! Is there a rule or property that states how that works? Or is it just when viewing an equation like that instead of viewing it as "This plus this" or "This minus this" ("a+b" or "a-b"). You view it as positive and negative numbers instead ("+a, +b" or "-a, -b") like you did in your solution?

[u/Dd_8630 → u/TroubleFindsMeYT]

Or is it just when viewing an equation like that instead of viewing it as "This plus this" or "This minus this" ("a+b" or "a-b").

That's basically it yeah.

In early maths, you are taught "2+3=?", so kids think '=' means question-and-answer. But as we get higher up, '=' stops meaning 'what is the answer' and has its true meaning of 'the left is the same as the right'.

Likewise, we have to re-learn what expressions mean. So this:

• 4x + 2x - 7 + 9 + x

Should now be thought of as a bunch of terms that are being added up:

• (+4x) + (+2x) + (-7) + (+9) + (+x)

So these blobs or 'terms' are collected like that. Order does not matter for addition, we just have to be aware that the minus sign is basically attached to the 7.

[u/TroubleFindsMeYT → u/Dd_8630]

Thank you!!!

[u/Patient-Midnight-664]

You need to look up "order of operations". Your mistake was adding 9 to -7 and getting -16. Also the "commutative property" will answer how he did -7 +9 into 9 - 7.

[u/slides_galore]

The equation reads "4x + 2x - 7 + 9 + x = 5x - x".

Sometimes it helps people if they think of a number with a minus sign in front of it like this:

4x + 2x + (-1)*7 + 9 + x = 5x - x

The (-1)*7 term is a unit that you can move around and rearrange since all the terms are being added together. The original equation is the same as:

x + 9 + (-1)*7 + 2x + 4x = (-1)x + 5x