when i talk about maths i always say conceptually clear maths, by this i mean ask on every question how and why. so we are going to start from Integers and work are way to linear equations
so what is an Integer ?
for that lets take a step back and ask ourselves what is natural and whole numbers
natural numbers - natural numbers are all the counting numbers, that we start counting from so that is from 1 and onwards
whole numbers - whole numbers are all the natural numbers but including 0
integers are all the negative and positive numbers plus 0 which is neither negative nor positive
now what is positive integers and negative integers
positive integers are all the numbers on positive side from 1
negative integers are all numbers on the negative side from -1
now lets look at some expressions
1) 2+6 = this means that i have +2 and i got a extra +6 so i am left with +8
+1 +1 +1 +1 +1 +1
* * * * * *
0--------1--------2--------3--------4--------5--------6--------7--------8
2) -4+2 = this means that i have -4 and i got +2 but i am left with -2
+1 +1
* *
(-4)--------(-3)---------(-2)---------(-1)---------0---------1---------2---------3---------4
3) -7-8 = this means that i have -7 but i also have -8 so i am left with -15
-1 -1 -1 -1 -1 -1 -1 -1
* * * * * * * *
---(-15)---(-14)---(-13)---(-12)---(-11)---(-10)---(-9)---(-8)---(-7)---(-6)---(-5)---(-4)---(-3)---(-2)---(-1)---0
4) 8-6 = this means that i have +8 but i have -6 so i am left with +2
-1 -1 -1 -1 -1 -1
* * * * * *
---(-6)---(-5)---(-4)---(-3)---(-2)---(-1)---0---1---2---3---4---5---6---7---8
5) 2-(-6) = these means that i have +2 and a extra +6
