Solving Equations
Example
Continued.
a
a
a
3
2
3
3
9
12
2
a
a
a
a
a
a
a
3
3
3
2
3
3
9
12
3
3
2
a
a
3
2
3
3
12
a
a
2
6
3
9
12
a
a
2
6
3
21
a
5
15
a
3
MartinGay,
Developmental Mathematics
56
Substitute the value for
x
into the original
equation, to check the solution.
Solving Equations
Example Continued
Since substituting the suggested value of
a
into the
equation produced undefined expressions, the
solution is
.
2
12
3
2
3
9
3
3
3
3
0
2
5
3
0
12
MartinGay,
Developmental Mathematics
57
Solving an Equation With Multiple Variables for
One of the Variables
1)
Multiply to clear fractions.
2)
Use distributive property to remove
grouping symbols.
3)
Combine like terms to simplify each side.
4)
Get all terms containing the specified
variable on the same side of the equation,
other terms on the opposite side.
5)
Isolate the specified variable.
Solving Equations with Multiple Variables
MartinGay,
Developmental Mathematics
58
2
1
1
1
1
R
R
R
2
1
2
1
2
1
1
1
1
R
RR
R
R
R
R
RR
1
2
2
1
RR
RR
R
R
2
1
2
1
RR
RR
R
R
2
2
1
RR
R
R
R
R
R
RR
R
2
2
1
Solve the following equation for R
1
Example
Solving Equations with Multiple Variables
Problem Solving with
Rational Equations
MartinGay,
Developmental Mathematics
60
Ratios and Rates
Ratio
is the quotient of two numbers or two
quantities.
The units associated with the ratio are important.
The units should match.
If the units do not match, it is called a
rate
, rather
than a ratio.
The ratio of the numbers
a
and
b
can also be
written as
a
:
b
, or
.
b
a
MartinGay,
Developmental Mathematics
61
Proportion
is two ratios (or rates) that are
equal to each other.
d
c
b
a
We can rewrite the proportion by multiplying
by the LCD,
bd.
This simplifies the proportion to
ad = bc.
This is commonly referred to as the
cross product
.
Proportions
MartinGay,
Developmental Mathematics
62
Solve the proportion for
x
.
3
5
2
1
x
x
2
5
1
3
x
x
10
5
3
3
x
x
7
2
x
2
7
x
Solving Proportions
Example
Continued.
MartinGay,
Developmental Mathematics
63
3
5
2
3
2
5
true
Substitute the value for
x
into the original
equation, to check the solution.
So the solution is
2
7
x
7
2
7
1
5
3
2
2
Example Continued
Solving Proportions
MartinGay,
Developmental Mathematics
64
If a 170pound person weighs approximately 65 pounds
on Mars, how much does a 9000pound satellite weigh?
Mars
on
satellite
pound

x
Mars
on
person
pound

65
Earth
on
satellite
pound

9000
Earth
on
person
pound

170
000
,
585
65
9000
170
x
pounds
3441
170
/
585000
x
Solving Proportions
Example
MartinGay,
Developmental Mathematics
65
Given the following prices charged for
various sizes of picante sauce, find the best
buy.
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 Fall '16
 Sherwin C. Lagrama
 Fractions, Fraction, Elementary arithmetic, Rational function