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Independent Practice: ALGEBRAIC PROPERTIES
NAME:
DATE:
PERIOD:
1) Solve the following and give a reason for each step.
90 = 3(2x-1)
Statements
Reasons
90 = 3(2x-1)
90 = 6x - 3
90 + 3 = 6x – 3 + 3
93 = 6x
93 6 x

6
6
15.5 = x
x = 15.5
2) Solve the following equation and give a statement or reason for each step.
5 = -3x – 16
Statements
Reasons
5 = -3x - 16
5 + 16 = -3x – 16 + 16
Simplify
Division Property of Equality
Simplify
x = -7
Geometry Unit 1 Essentials of Geometry
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Independent Practice: ALGEBRAIC PROPERTIES
Solve the following equations, use the statements to determine the reason for
each step.
3) 2x  15  90
Statements
Reasons
2x  15  90
2x  15 15  90 15
2x  75
2 x 75

2
2
x  37.5
4)  5x 12  180
Statements
Reasons
 5x  12  180
 5x  12  12  180  12
- 5x  192
 5 x 192

5
5
x  38.4
Geometry Unit 1 - Essentials of Geometry
Page 6
Independent Practice: ALGEBRAIC PROPERTIES
Solve the following equation and give a statement or reason for each step.
5) 90 
4x  2
5
Statements
90 
Reasons
4x  2
5
Multiplication Property of Equality
Simplify
450  2  4x  2  2
452  4x
Division Property of Equality
113 = x
Symmetric Property
6)
 3x  5
 45
2
Statements
Geometry Unit 1 - Essentials of Geometry
Reasons
Page 7
Independent Practice: ALGEBRAIC PROPERTIES
Solve the following equation and give a statement and a reason for each step.
7)  3(2 x  5)  18
Statements
Reasons
8) 3x `162  180
Statements
Reasons
On a separate sheet of paper, solve the following equations. Give a
statement and a reason for each step.
9) 5(4  16 x)  180
10) 2(3x  4)  2 x  90
11) 4 x  5  ( x  2)  90
Geometry Unit 1 - Essentials of Geometry
12)  3x 19  2x  90
 2  16 x
 5 x  180
4
14) 45  3x  (7  x)
13)
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