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Question 1013568: I need help with Inequalities and solving the equation.
I don't get it so if you can please explain it step by step that would be amazing!
Here are some examples:
1. 12 = 2x + -8y
2. 3(x+-4) + -2(2x+4y) = -8(3-x)
3. 3x + 5y = 12y + 2
Thx in advanced
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Maybe you need help with negative numbers.
What you posted are linear  tions, because they have an  sign.
They are not inequalities.
Inequalities have  , or  , or  , or  signs.
The last two equations need a little simplifying.
 is the equation of a line that goes through points (6,0) and (0,-3/2).
When  ,  --> ---> , so we get point (6,0), with  .
When  ,  --> ---> ---> , so we get point (0,-3/2), with  .
 is an inequality that represents the half of the x-y plane below the line representing .
 is an inequality that graphs as the line representing and the half of the x-y plane below that line.
All those "-" signs probably mean that your teacher is trying to make you see that negative numbers exist.
If you lived in a northern cold place, you would believe in negative numbers,
because you would be seeing them in your outdoor thermometer.
When you take  steps "forward" and  steps "back",
your advance in the intended direction is  .
In elementary school, they told you that is subtraction :  ,
read as "3 minus 2 equals 1".
In college, they told me that there was no such thing as subtraction,
that taking away is really adding  ,
and that was the opposite of ,
because adding them together I would get  ,
which was the number that added to anything caused no change at all.
So I stopped believing in subtraction,
just as I had stopped believing in Santa Claus and the tooth fairy,
and the next day, for my father's birthday, I told him that as a poor student, all I could give him as a birthday gift was  ,
and he gave me the $20 I needed.
Normally, we write  or 
as  to save ink.
We simplify it by applying the distributive property as needed:
 ,
and do the multiplications first:
(Normally, we write the equation above as
 to save ink).
Next we "collect like terms"
by changing the order of those terms (commutative property of addition),
--->
and "taking ot the common factor" (applying the distributive property)
---> --->
Since we have terms in  on both sides of the equal sign,
and terms without any variable on both sides of the equal sign,
we want to add opposite terms to both sides of the equal sign as needed to simplify this mess.
--->
That is the equation of a line that passes through the points with
 --> --> and
 --> --> .
 can be simplified by adding  to both sides of the equal sign to get
 or 
That is the equation of a line that passes through the points with
 --> --> and
 --> .
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