Algebra

Front 1

Properties of negatives

Back 1

1. - (-X)= X
2. (-x) = (-y)= -(x+y)
3. x - y = x = (-y)
4. (-1)x= -x
(-x)y = x(-y) = -xy
(-x)(-y)= xy
5. -x/y = x/-y = - x/y provided y does not equal 0

Front 2

absolute value

Back 2

if x is a real number
|x| = x if x > 0
|x| = -x if x < 0

Front 3

distance between two points

Back 3

if a and b are coordinates of two points on a number line, then the distance between those points is given by the formulas

d= |a - b| or d= |b-a|

Front 4

the trichotomy property

Back 4

for any two real numbers a and b, exactly one of the following relationships must hold:

a = b or a<b or a>b

Front 5

properties of equality

Back 5

if a, b, and c are real numbers, then
a =a (reflexive property)
if a=b, then b=a (symmetric property)
if a=b and b=c then a=c (transitive property)