These are the
multiplication and division properties of equality
Ø
If
? = @
, then
? ⋅ A = @ ⋅ A
and
C
=
D
C
.
Ø
Give examples of this property.
.
B

Section 2: Equations and Inequalities
33
Try It!
2.
The following pairs of equations are equivalent. Determine
the property that was used to write the second equation.
1.
For each algebraic equation, select the property or
properties that could be used to solve it.
a.
2
6 + 4
= 14 − 66
and
26 + 8 = 14 − 66
b.
26 + 8 = 14 − 66
and
26 + 8 + 66 = 14 − 66 + 66
c.
26 + 8 + 66 = 14
and
26 + 66 + 8 = 14
d.
86 + 8 = 14
and
86 + 8 − 8 = 14 − 8
e.
86 = 6
and
+
.
⋅ 86 =
+
.
⋅ 6
BEAT THE TEST!
Algebraic Equation
Addition or Subtraction
Property of Equality
Multiplication or Division
Property of Equality
Distributive Property
Commutative Property
;
,
= 5
o
o
o
o
26 + 7 = 13
o
o
o
o
46 = 23
o
o
o
o
6 − 3 = −4
o
o
o
o
4(6 + 5) = 40
o
o
o
o
10 + 6 = 79
o
o
o
o
−8 − 6 = 19
o
o
o
o
2(6 − 8) + 76 = 9
o
o
o
o
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Section 2: Equations and Inequalities
34
A word problem or situation may require you to write and
solve an equation.
Jenna is applying to The Citadel, The Military College of South
Carolina. Jenna wants to achieve a minimum score on the SAT
Reasoning Assessment to be a competitive applicant.
Jenna has earned a score of
980
on the SAT and has signed
up for a test prep class to help her improve her score. The test
prep company claims that each class she attends will increase
her score by
10
points.
Identify the variable in this situation.
Assuming the company’s claim is correct, write an expression
to represent Jenna’s SAT score after she attends any given
number of classes.
The average SAT score for incoming freshman at The Citadel is
1070
. Suppose the test prep company’s claim is correct and
her score will increase by
10
points for each class that she
attends. Write and solve an equation to determine the
number of classes Jenna must take in order to earn the
average score.
Sarah is an engineer for the Fluor Corporation, an engineering
and construction company in Greenville. She needs to
calculate how long it will take to remove
6,000
gallons of
water from a drainage ditch at a construction site using three
water pumps. Used alone, Pump A can remove all of the rain
water in four hours, while Pump B will take three hours. Sarah
wants to run Pump A, Pump B, and Pump C simultaneously to
remove the water in one hour.
The equation below models the three pumps working together
to remove the water in one hour, where
6
represents the
number of hours Pump C will take to remove the rain water by
itself.
1
4
+
1
3
+
1
6
= 1
Use the box below to determine the number of hours Pump C
will take to remove the rain water by itself.
Justify each step.
Section 2 – Topic 3
Solving Equations