AbsoluteValv tiven
2 real numbers a k b we
the distant between them using
1 1 is defined as
e.g
the
distance
The set of
D
between
39
can
calculate
where
2 is
numbers
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than
f
numbersDthatareadistauie less
unit away from the number
U
also written
can
a
be visualized
D
as
more generally
If
ve
A
and
the strict inequality to
get the set of points
we change
very very
absolute
common
tool
values
is
Theory
For
any
a
b
c
ER
that
is used
D
with inequalities
An
arguably more
useful
version
is
given
by
theorem
Emo
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Ex Show that latbl lol
i
A
more
general
E
lat b
definition of
c
absolute value is
given by
Solve the inequalities
Ey
1 2 41 3
1 11 51 1124
ask.tk
11
X
Cast
then
Assume
our
inequality becomes
sithotthesesatistionasiumptionothenthe
are
both valid
Casf
Assumed
then
whish gives
j.thnthiisdsor.li
The solution set
is
1 11
b
51 1 24
Consider
Case
A
X I
number line
the
I
D
then
thus
Case B
and
thus
get
all of xet
f
lox El then
we
and
we
we
get
have
sin
into
thn
Final
answer is
D
we have
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