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SOL A.4.b - Properties
Contribució de: Terrazas
(Autor original: Tilashalski)
Unit 2 Test
A.4.b:
Properties used to solve equations:
Distributive
Commutative
Equality, Inverse, Identity
Identify the properties that justify the work donebetween step 2 and step 3. 
Addition property of Equality.
Distributive Property
Additive Identity
Additive Inverse
Step 1:             3x + 5 = -1
Step 2:   3x + 5 + (-5) = -1 + (-5)
Step 3:             3x + 0 = -6
Step 4:                   3x = -6
Identify the property that justifies the work 
between steps 1 & 2.
Division Property of Inequality
Commutative Property
Distributive Property
Additive Inverse
Step 1:     2(4 + x) ≥ -2
Step 2:     2(4 + x) ≥ -2
                      2          2
Identify the properties that justify each step. 
Step 1:                   3x  = -6Step 2:                ⅓(3x) = ⅓(-6)Step 3:                    1x = -2Step 4:                      x = -2
Between Step 1 & 2:
Between Step 2 & 3:
Between Step 3 & 4:
Multiplicative Equality
?
Multiplicative Inverse
?
Multiplicative Identity
?
Identify the properties that justify each step. 
            3(x + 1)  = -12                 given            3x + 3    = -12     3x + 3+(-3) = -12+(-3)               3x + 0 = -15                     3x = -15                     3x = -15                     3         3                     1x = -5                       x = -5
Equality of Division
?
Multiplicative Inverse
?
Multiplicative Identity
?
Equality of Addition
?
Additive Inverse
?
Additive Identity
?
Distributive Property
?
Identify the property that justifies the work between
steps 1 & 2.
Multiplication Property of Inequality
Multiplication Property of Equality
Distributive Property
Additive Inverse
Step 1:     2(3 + 2x) = 1Step 2:         6 + 4x = 1
Identify the property that justifies the work 
between steps 2 & 3.
Division Property of Inequality
Division Property of Equality
Distributive Property
Multiplicative Inverse
Step 1:     2(4 + x) ≥ -2Step 2:     2(4 + x) ≥ -2                      2          2Step 3:     1(4 + x) ≥ -2
Based on the Multiplicative Inverse property, 
fill in the blank.
Step 1:        2x ≥ 10Step 2:    ½(2x) ≥ ½(10)Step 3:           x ≥ 5

Determine which property was incorrectly used forjustifying the steps and name the correct property that should have been used:
Step 1          4x=-3      GivenStep 2     ¼(4x)=¼(-3)  DistributiveStep 3         1x = -¾     Multiplicative InverseStep 4           x = -¾     Multiplicative Identity
Step 2; Equality of Division
Step 2; Equality of Multiplication
Step 3; Multiplicative Identity
Step 3; Additive Identity
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