Download Simplify Algebraic Expressions

Teacher Key
Algebra
Simplify Algebraic Expressions
Name the property that explains why each equation is true.
A. 4x + (3 + 2x) = 4x + (2x + 3)
B. 6b + (3b + 5) = (6b + 3b) + 5
Commutative Property of Addition
Associative Property of Addition
Distributive Property
C. 8 + 2(x –3) = 8 + 2x – 6
D. (3 + 2y) + (4y + 8) = 3 + (2y + 4y) + 8
E. (6a + 5) + 2a = (5 + 6a) + 2a
Associative Property of Addition
Commutative Property of Addition
Simplify the algebraic expression. Show your work.
F. 3x + 6 – x = 3x + 6 + (-x)
= 3x + (-x) + 6
= 2x + 6
H. (18 ÷ 6) – 2t + 5 =
J. 2(r – 3) + 4(3 – r) =
L. 2x – y + 5 y –1 =
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3 – 2t + 5
= 3 + (-2t) + 5
= 3 + 5 + (-2t)
= 8 + (-2t)
= 8 – 2t
2r – 6 + 12 – 4r
= 2r + (-6) + 12 + (-4r)
= 2r + (-4r) + (-6) + 12
= -2r + 6
2x + (-y) + 5y + (-1)
= 2x + 4y + (-1)
= 2x + 4y – 1
G. 12(x – 4) + 3x =
12x – 48 + 3x
= 12x + (-48) + 3x
= 12x + 3x + (-48)
= 15x + (-48)
= 15x – 48
I. 5 – 2b + 5 – b =
5 + (-2b) + 5 + (-b)
= 5 + 5 + (-2b) + (-b)
= 10 – 3b
K. 4a + 4 – 2a – 3 =
M. 6b + 5(3 – b) =
4a + 4 + (-2a) + (-3)
= 4a + (-2a) + 4 + (-3)
= 2a + 1
6b + 15 – 5b
= 6b + 15 + (-5b)
= 6b + (-5b) + 15
= b + 15
Activity 67205
Teacher Key
Algebra
Connections
Think About It
In an algebraic expression, like terms are combined. So, in an algebraic equation such as
2x + 6 + x = x + 2, is combining like terms still allowed?
SAMPLE
RESPONSE: Only the like terms on 1 side of the equation may be
________________________________________________________________________
combined.
In order to maintain the equality of the 2 expressions, use inverse
________________________________________________________________________
elements
to combine like terms from the other side of the equal sign. This will allow
________________________________________________________________________
you
to solve for the value of the unknown variable.
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2x + 6 + x = x + 2
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3x + 6 = x + 2
3x
+
6 – x = x + 2 – x To combine the variables, x must
________________________________________________________________________
2x + 6 = 2
be subtracted from each side.
To
combine
the
numbers,
6
must
x
+
6
–
6
=
2
–
6
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be subtracted from each side.
2x = -4
x = -2
________________________________________________________________________
Expression Search
Find the simplified expression for each algebraic expression in the bank. The simplified
expressions may be found vertically or horizontally.
Bank
5a – 2 + 7 – 2a
3
a
+
5
7
+
k
4
d
3
2(2b –3) + c
b
+
4
-
6
h
2
5
0
-
5(1 + b) - 3b – 4
8
a
1
7
1
2
b
-
1
0
2d + 3 + 6d
d
d
1
-
0
8
+
7
c
3
(5 + 6d) – 2d – 5
+
6
k
7
-
2
1
+
1
b
2 + 5k + 6k – 6
3
1
-
+
7
b
+
8
5
9
a
6
4
0
c
4
7
3
-
k
-
9
c
-
6
+
k
3
3
c
4
b
+
c
-
6
2
b
a
+
2c(8 + 8) + c
3(5 – a)
(2 x 5) + 3 c – 10c
2(6b – 5)
© 2003 CompassLearning, Inc.
Activity 67205