# x +-x = ? 0? Plus a few more...

##### New member
I took home a 100 question test of algebra questions today...due back in 5 days So, I have a couple questions. If anyone could help me it would be greatly appreciated!

#1 - (x-6)-(x+8)=9x How do I eliminate the parenthesis? Do I solve it by just removing the parenthesis, which leaves x-6-x+8=9x? From there I combine like terms, which makes me discover something: what is x+-x? Since x has a coefficient of 1, isn't it 0? But an unknown number and a negative unknown number isn't always 0, so :?: I have four answer choices: A)-7/2 B)-14/9 C)-7/3 D)-1/9 Any way I solve it I don't get any of these. :? Thanks for your help.

#2 - A similar problem to #1, but lengthier. -3(x+3)-(4x-6)=-9 I think what's confusing me in all of these are those parenthesis. I'm supposing I just remove them. Doing that, I get here: -3x+-9-4x-6=-9 What do I do with those two +- signs? Or did I do something wrong?

#### tkhunny

##### Moderator
Staff member
One at a time, Fellow Pennsylvanian!
#1 - (x-6)-(x+8)=9x How do I eliminate the parenthesis?
You must practice the Distributive Propoerty of Multiplication over Addition.

- (x-6) = -x + 6

-(x+8) = -x - 8

Putting it all together.

- x + 6 - x - 8 = 9x

what is x+-x? Since x has a coefficient of 1, isn't it 0? But an unknown number and a negative unknown number isn't always 0, so
You almost have the right idea. The only problem is that you do not have the right definition of 'x'. Do not think of it as just some unknown number. It IS a number. We just don't know which ONE. In a single equation, any reference to 'x' must refer to the same number. x - x is ALWAYS zero (0), since x = x in any single equation. It doesn't mean some other 'x' because it appears later in the equation.
#2 - A similar problem to #1, but lengthier. -3(x+3)-(4x-6)=-9
Just one piece at a time.

-3(x+3)-(4x-6)=-9
-3x - 9 - (4x-6) = -9
-3x - 9 - 4x + 6 = -9

That's how you get rid of parentheses - carefully and remembering the distributive property of multiplication over addition.

##### New member
tkhunny said:
One at a time, Fellow Pennsylvanian!
#1 - (x-6)-(x+8)=9x How do I eliminate the parenthesis?
You must practice the Distributive Propoerty of Multiplication over Addition.

- (x-6) = -x + 6

-(x+8) = -x - 8

Putting it all together.

- x + 6 - x - 8 = 9x

what is x+-x? Since x has a coefficient of 1, isn't it 0? But an unknown number and a negative unknown number isn't always 0, so
You almost have the right idea. The only problem is that you do not have the right definition of 'x'. Do not think of it as just some unknown number. It IS a number. We just don't know which ONE. In a single equation, any reference to 'x' must refer to the same number. x - x is ALWAYS zero (0), since x = x in any single equation. It doesn't mean some other 'x' because it appears later in the equation.
[quote:23av8pal]
#2 - A similar problem to #1, but lengthier. -3(x+3)-(4x-6)=-9
Just one piece at a time.

-3(x+3)-(4x-6)=-9
-3x - 9 - (4x-6) = -9
-3x - 9 - 4x + 6 = -9

That's how you get rid of parentheses - carefully and remembering the distributive property of multiplication over addition.[/quote:23av8pal]

*shakes hand* Good day, neighbor! I see we live in the same state! Thanks for clarifying that. Oh dear, I just didn't see that...I knew how to do that, but now I see I just wasn't thinking. :roll: Very easy. And about the x-(+x)=0, that made a lot of sense when you said that x always equals x in a single equation. I used to have major trouble with those x's. Now I'm a bit better with them, but still...

And is it true that the coefficient of x is 1? I heard that once, from a friend or something, but is that any truth?[/i]

#### tkhunny

##### Moderator
Staff member
Coefficient of 1. Yes. Normally, it should not be written. If you need to write it, while you get used to it, that is fine.

#### Subhotosh Khan

##### Super Moderator
Staff member
I took home a 100 question test of algebra questions today...due back in 5 days So, I have a couple questions. If anyone could help me it would be greatly appreciated!
Should you be asking for help on a test?

##### New member
Subhotosh Khan said:
I took home a 100 question test of algebra questions today...due back in 5 days So, I have a couple questions. If anyone could help me it would be greatly appreciated!
Should you be asking for help on a test?
It's a take-home, and I'm allowed to use my TI83 calc. on it, which alone would give me answers if I wanted to only use it instead of figuring out the problem, which is why I'm here. I also am allowed to ask the professor any questions I have on the test the day before I hand it in, and I'm allowed to ask my classmates about any questions I have. Yep, my professor is rather lenient... But, the in-class test is very different. We have 50 minutes to do it and it's about 60 questions. If I can understand the problems in my take-home, the in-class test will be easier.

#### Denis

##### Senior Member
Well meLady, for this type, simply remember:
if sign before brackets is +, simply remove brackets :
a + (b - c) = a + b -c , a + (-b - c) = a - b - c

if sign is -, remove brackets but change ALL inside signs:
a - (-b - c) = a + b + c

There is a theoretical "1" in front of brackets: 1(a - b);
removing the brackets is simply multiplying by 1: 1 * a + 1 * (-b) = a - b;
same as 2(a - b): 2a - 2b