b. Solve using the procedures that produce equivalent equations.
– 9
.
.
cont’d
SOLUTION
Classify each equation as a contradiction, a conditional equation, or an identity.
5
ABSOLUTE VALUE EQUATIONS
DEFINITION
The absolute value of a number
a
is given by
ABSOLUTE VALUE EQUATIONS
.
line
number
real
the
on
a
and
x
between
ce
tan
dis
the
is
a
x
,
generally
More
.
origin
the
to
a
of
ce
tan
dis
the
represents
it
that
and
0
a
if
a
0
a
if
a
a
ABSOLUTE VALUE EQUATIONS
The following property is used to solve absolute value equations.
A Property of Absolute Value Equations
For any variable expression
E
and any nonnegative real number
k
,

E

=
k
if and only if
E
=
k
or
E
= –
k
ABSOLUTE VALUE EQUATIONS
EXAMPLE
If 
x
 = 5, then
x
= 5 or
x
= –5.
If 
x

=
, then
x
=
or
x
= –
.
If 
x
 = 0, then
x
= 0.
ABSOLUTE VALUE EQUATIONS
SOLVE AN ABSOLUTE VALUE EQUATION
Solve:  2
x
– 5  = 21
Solution:
 2
x
– 5  = 21 implies 2
x
– 5 = 21 or 2
x
– 5 = –21.
Solving each of these linear equations produces
2
x
– 5 = 21
or
2
x
– 5 = –21
2
x
= 26
2
x
= –16
x
=
13
x
=
–8
SOLVE EACH EQUATIONS
14
5
7
3
.
2
3
5
2
.
1
x
x
2
3
1

x
.
4
15
6
5
3
.
3
x
x
FORMULAS
Table 1.2
Formulas from Geometry
FORMULAS
It is often necessary to solve a formula for a specified variable.
Begin the process by isolating all terms that contain the specified
variable on one side of the equation and all terms that do not
contain the specified variable on the other side.
FORMULAS
a
.
Solve
2
l
+ 2
w
=
P
for
l
.
b.
Solve
S
= 2(
wh
+
lw
+
hl
) for
h
.
Solution:
P
w
SOLVE A FORMULA FOR A SPECIFIED VARIABLE
EXAMPLE
b
.
S
= 2(
wh
+
lw
+
hl
)
S
= 2
wh
+ 2
lw
+ 2
hl
S
– 2
lw
= 2
wh
+ 2
hl
S
– 2
lw
= 2
h
(
w
+
l)
cont’d
You've reached the end of your free preview.
Want to read all 77 pages?
 Spring '12
 edgar
 Math, Equations, Elementary algebra, ESTRADA, Division Property of Equality