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Chapter 2: B. Basic Algebra 13
Table 2.1 Additional properties of real numbers.
Property
Reflexive property
Symmetric property
Transitive property
Additive identity
Multiplicative identity
Example
a = a
If a = b, then b = a
If a = b and b = c, then a = c
a + 0 = a
a × 1 = a
Part I.B
Table 2.2 Inverse operations.
Operation Inverse operation Example
Addition Subtraction a+ ( a)= 0
Subtraction Addition a+ a=
0
1
Multiplication Division a × = 1
a
Division Multiplication (×)
1
× a = 1
a
r r
Exponent r rth root a = a,fora
0
r
( ) =
r
rth root Exponent r a a,fora
0
Power of 10 Log base 10 log 10 ( 10 a )= a
log (
Log base 10 Power of 10 10 10 a) = a
Solving Equations Using One Inverse Operation
In order to isolate x, we perform the appropriate inverse operation on both sides of
the equation. In the example below, note that the inverse of adding 3 is subtracting
3:
x + 3=
5
x + 3 3= 5
3
x = 2