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SOL A.4.b - Properties Retake
Contributed by: Kaur
(Original author: 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 3 and step 4. 
Addition property of Equality.
Distributive Property
Additive Identity
Additive Inverse
Step 1:             2x + 5 = -1Step 2:   2x + 5 + (-5) = -1 + (-5)Step 3:             2x + 0 = -6Step 4:                   2x = -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(2 - x) ≥ -2Step 2:     4 - 2x≥ -2                    

Identify the property

If x + 1 = 2 and 2 = y, then x +1 = y

reflexive property

transitive property

symmetric property

commutative property

 
Identify the properties that justify each step. 
            -2(a + 1)  = -12                 given            -2a - 2    = -12            -2a -2+2 = -12 + 2               -2a + 0 = -10                     -2a = -10                     -2a = -10                     -2         -2                     1a = 5                       a = 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

Commutative Property

Step 1:   3(x + 4) +x = (3x + 12 ) +x Step 2:                        (12 + 3x ) + xStep 3:                         12 + (3x + x)Step 4:                         12 + 4x   
 
Identify the property that justifies the work 
between steps 2 & 3.

Associative property of addition

Commutative property of Addition

Distributive Property
Multiplicative Inverse
Step 1: 3(x + 4) +x = (3x + 12 ) +x Step 2: (12 + 3x ) + xStep 3: 12 + (3x + x)Step 4: 12 + 4x
Which equation below represent second step of the solution process.
 -6x - 3 + 6 = 45

-3 (2x + 7) = 45

-6x + 1 + 6 = 45

-3(2x + 6) + 1 = 45

Step1: -3(2x + 1 ) + 6 = 45

Step 2:

Step 3: -6x + 3 = 45

Step 4: -6x = 42

Step 5: x = -7

Determine which property was incorrectly used forjustifying the steps and name the correct property that should have been used:
Step 1          ⅓x=24      GivenStep 2     3 (⅓ x) = 3(24)  Equality of multiplicationStep 3         1x = 72     Additive InverseStep 4           x = 72     Multiplicative Identity
Step 2; Equality of Division
Step 2; Equality of Multiplication
Step 3; Multiplicative Inverse
Step 3; Additive Identity
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