My Math Forum Algebra confusion , linear equation

 Algebra Pre-Algebra and Basic Algebra Math Forum

 March 13th, 2009, 06:55 PM #1 Member   Joined: Feb 2009 Posts: 52 Thanks: 0 Algebra confusion , linear equation So im doing point slope formulas and my book nails me with this question Find and equation for this line, write ansers in slope-intercept form. Through (-1, 3) with slope -2 Y - 3 = -2(x - (-1) ) I highlighted the part that confuses me. Apparently the CORRECT next step is Y - 3 = -2 (x + 1) however im getting Y - 3 = -2x - 1 Why is it that x - (-1) = 1 when -3 - (-1) = -4 ? typically ive been handling variables as being a postive 1 in equations IE x(4) = 4 my instructor said something about double negatives becoming a positive but im just trying to understand why since this is not multiplication or division.
 March 13th, 2009, 07:05 PM #2 Newbie   Joined: Mar 2009 Posts: 11 Thanks: 0 Re: Algebra confusion , linear equation y - 3 = -2(x - (-1)) the next part is y - 3 = -2(x+1) because it's like saying "the opposite of negative 1 is positive one. One trick that I learned is that if there is something like (x - (-1)). you just take the negative after the x and put it perpendicular over the negative in front of the 1 to make it a positive sign
March 13th, 2009, 07:33 PM   #3
Member

Joined: Feb 2008

Posts: 89
Thanks: 0

Re: Algebra confusion , linear equation

Quote:
 Originally Posted by roncarlston Why is it that x - (-1) = 1 when -3 - (-1) = -4 ? typically ive been handling variables as being a postive 1 in equations IE x(4) = 4 my instructor said something about double negatives becoming a positive but im just trying to understand why since this is not multiplication or division.
Greetings:

To your first question, -3 - (-1) is NOT= -4. -3 - (-1) = -2. Recall that to subtract a number, is to add its opposite; that is, a-b = a+(-b). So, -3 - (-1) is equivalent to adding the opposite of -1 to -3. I.e., -3 - (-1) = -3 + 1 = -2. Similarly, therefore, x - (-1) = x + 1.

Another way to view this is via the distributive property. To that end, -2(x - (-1)) = -2*x - (-2*-1) = -2x - 2 = -2(x+1).

Regards,

Rich B.
rmath4u2@aol.com

 March 13th, 2009, 07:45 PM #4 Member   Joined: Feb 2009 Posts: 52 Thanks: 0 Re: Algebra confusion , linear equation Thanks to the first poster for that little visual trick and thanks nikko for pointing that out. so, technically we treat x or any variable as being zero? ( i know it seems obvious since a lot of the time we figure out and assign a value to a variable) but i had read somewhere (perhaps misread) in my algebra book that you can think of variables as being 1 or having a 1 next to them so when i am seeing X - (-1) i am thinking 1 - (-1) = 2
March 13th, 2009, 08:47 PM   #5
Newbie

Joined: Mar 2009

Posts: 11
Thanks: 0

Re: Algebra confusion , linear equation

Quote:
 so when i am seeing X - (-1) i am thinking 1 - (-1) = 2
yup. the same thing as saying "x minus the opposite of negative one. a negative minus a negative will always be a positive

how is that false?

March 13th, 2009, 09:21 PM   #6
Member

Joined: Feb 2009

Posts: 52
Thanks: 0

Re: Algebra confusion , linear equation

Quote:
Originally Posted by achmeineye
Quote:
 so when i am seeing X - (-1) i am thinking 1 - (-1) = 2
yup. the same thing as saying "x minus the opposite of negative one. a negative minus a negative will always be a positive

wait what? a negative minus a negative will always be positive?

now i am really confused.

March 13th, 2009, 10:23 PM   #7
Senior Member

Joined: Feb 2009

Posts: 1,519
Thanks: 3

Re: Algebra confusion , linear equation

Quote:
 wait what? a negative minus a negative will always be positive?

In the following I'm going to use the letter y instead of the letter x, so that it doesn't look like a multiplication sign.

- 2(y - (-1))

Taking minus one is the same as adding plus one. So it simplifies into:

- 2(y + 1)

What happens if you don't simplify before multiplying? Then you do this:

[color=red]- 2[/color] (y [color=blue]–[/color] [color=green](-1)[/color] )

= [color=red](- 2)[/color] y [color=blue]–[/color] [color=red](-2)[/color] [color=green](-1)[/color]

There are three successive minus signs.

"Minus times minus" is plus, so... minus times (minus times minus) = minus times plus = minus.

- 2 y - 2

You said above that "this isn't multiplying." Yes it is! You're multiplying by ONE or MINUS ONE, so you don't see the multiplication, because it isn't normally written in.

-(-y) = -1 ( -1 y) = (-1*-1) y = y

 March 14th, 2009, 05:03 AM #8 Senior Member   Joined: Mar 2009 Posts: 318 Thanks: 0 It sounds like you're having trouble with negative numbers and taking them "through" parentheses, so you might want to brush up on these topics. [color=white]. . . . .[/color]Google results for "negative numbers" [color=white]. . . . .[/color]Google results for "simplify parentheses" Pick a couple of lessons from each link, and study their worked examples. Then see if the steps for your posted exercise make a little more sense.
March 15th, 2009, 09:09 AM   #9
Global Moderator

Joined: Dec 2006

Posts: 20,104
Thanks: 1907

Quote:
 Originally Posted by roncarlston . . . my instructor said something about double negatives becoming a positive, but I'm just trying to understand why, since this is not multiplication or division.
There's a version of the rule about double negative becoming positive that applies to subtraction; it says that p - (-q) becomes p + q.

March 15th, 2009, 12:54 PM   #10
Senior Member

Joined: Mar 2009

Posts: 318
Thanks: 0

Quote:
 Originally Posted by skipjack There's a version of the rule about double negative becoming positive that applies to subtraction; it says that p - (-q) becomes p + q.
But p - (-q) = p - 1(-q) = p + (-1)(-q), so it's kinda still multiplication....

 Tags algebra, confusion, equation, linear

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post matqkks Linear Algebra 1 February 7th, 2012 02:39 PM daigo Algebra 3 February 2nd, 2012 05:10 PM SkyDiver Algebra 7 October 12th, 2009 07:23 AM ypatia Linear Algebra 2 March 5th, 2009 02:49 PM ypatia Linear Algebra 1 March 2nd, 2009 07:28 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top