Consider the statement
4 + 5 = 2 + 7
. This is a grammatically
correct sentence.
Is the sentence true or false?
Consider the statement
1 + 3 = 8 + 6
. This statement is also a
grammatically correct sentence.
Is the sentence true or false?
The previous statements are examples of
number sentences
Ø
A number sentence is a statement of equality
between two __________________ expressions.
Ø
A number sentence is said to be true if both numerical
expressions are ___________________.
Ø
If both numerical expressions don’t equal the same
number, we say the number sentence is ____________.
.
Ø
True and false statements are called
truth values
.

Section 2: Equations and Inequalities
30
Let’s Practice!
3.
Consider the algebraic equation
6 + 3 = 9
a.
What value can we substitute for
6
to make it a true
number sentence?
b.
How many values could we substitute for
6
and have
a true number sentence?
4.
Consider the algebraic equation
6 + 6 = 6 + 9
. What
values could we substitute for
6
to make it a true number
sentence?
Try It!
5.
Complete the following sentences.
a.
8
,
= 4
is true for _________________________.
b.
29 = 9 + 9
is true for _________________________.
c.
8 + 67 = 8 + 68
is true for _________________________.
A number sentence is an example of an
algebraic equation
Ø
An algebraic equation is a statement of equality
between two __________________.
Ø
Algebraic equations can be number sentences (when
both expressions contain only numbers), but often
they contain ________________ whose values have not
been determined.
Consider the algebraic equation
4
6 + 2
= 46 + 8
Are the expressions on each side of the equal sign equivalent?
Justify your answer.
What does this tell you about the numbers we can substitute
for
6
.
.
.
?

Section 2 – Topic 2
Identifying Properties When Solving Equations
The following equations are equivalent. Describe the
operation that occurred in the second equation.
1.
Which of the following equations have the correct
solution? Select all that apply.
,
BEAT THE TEST!
Want some help? You can always ask questions on
the Algebra Wall and receive help from other

Section 2: Equations and Inequalities
31
Algebra
Wall
students, teachers, and Study Experts. You can also
help others on the Algebra Wall and earn Karma
Points for doing so. Go to AlgebraNation.com to learn
more and get started!

Section 2: Equations and Inequalities
32
Let’s Practice!
1.
The following equations are equivalent. Determine the
property that was used to write the second equation.
a.
6 − 5 = 36 + 7
and
6 − 5 + 5 = 36 + 7 + 5
b.
6 = 36 + 12
and
6 − 36 = 36 − 36 + 12
c.
−26 = 12
and
E,;
E,
=
+,
E,
If
6
is a solution to an equation, then
6
will also be a solution to
the new equation formed when the same number is
added to
each side of the original equation.
These are the
addition and subtraction properties of equality
Ø
If
? = @
, then
? + A = @ + A
and
? − A = @ − A.
Ø
Give examples of this property.
If
6
is a solution to an equation,
6
will also be a solution to the
new equation formed when each side of the original equation
is multiplied by the same number.
Properties of Equality
.