SOL A.4.b,d,f Test Review
Unit 2 Test Review

SOL. A.4.b
The student will solve multi-step linear and quadratic
equations and inequalities in two variables, including
justifying steps used in simplifying expressions and
solving equations and inequalities, using field
properties and axioms of equality that are valid for the
set of real numbers and its subsets.

SOL A.4.d
The student will solve multi-step linear and quadratic
equations in two variables, including solving multi-step
linear equations algebraically and graphically.

SOL A.4.f
The student will solve multi-step linear and quadratic
equations in two variables,including solving real world
problems involving equations.
Between Step 1 & 2:

Between Step 2 & 3:

Between Step 3 & 4:


Identify the properties that justify each step.
Step 1: -8 = n + 3
Step 2: -8 - 3 = n + 3 - 3
Step 3: -11 = n + 0
Step 4: -11 = n
Subtraction Property of Equality
?
Additive Identity
?
Additive Inverse
?
Identify the property that justifies step 1 to step 2.
Step 1: 13x -1=(12x+15)+7x
Step 2: 13x - 1= 7x + (12x +15)
Associative property of addition
Identity property of addition
 Commutative property of addition
Distributive property
Between step 1 and step 2:

Between step 2 and step 3:

Between step 3 and step 4:
Identify the properties that justify each step.
Step 1:    2x = -8
Step 2:    ½(2x) = ½(-8)
Step 3:    1x = -4
Step 4:     x = -4
Multiplicative Identity
?
Multiplicative Inverse
?
Equality of Multiplication
?
Between step 1 and step 2:

Between step 3 and step 4:

Between step 4 and step 5:
Identify the properties used to justify each step.
Step 1:                 2x = -3(4x - 2) + 1
Step 2:                 2x = -12x + 6 + 1
Step 3:
                2x = -12x +7
Step 4:      2x + 12x = -12x +12x + 7
Step 5:               14x = 0 + 7
Additive Inverse
?
Equality Property of Addition
?
Distributive Property
?
What is the solution to 3(2x-1) = 3?
x =
What is the solution to:  2x-2 = -4   ?
                                        3
x =
What is the solution to:

   3(2m-1) = 3m +12
m=
What is the solution to:

    4(x + 7) = 4x - 3
x = - 31
infinite solutions
no solution
x = 25
x = 0
x = 3
What is the solution to

-5(2x-3) = -8x + 15 - 2x
Infinite Solutions
No Solution
Select the algebraic expression that is represented
by the algebra tiles below.
 2x + 5 = -4x - 3
2x - 5 = -4x + 3
+
+
-2x -5 = 4x +3
2x = 4
+
+
+
4 inches
10 inches
The length of a rectangle is 4 inches more
than its width. The perimeter of the rectangle
 is 40 inches. Select the two dimensions of the
rectangle.
14 inches
12 inches
20 inches
8 inches
The width of a rectangle is 3 inches less than
its lenth. The perimeter of the rectangle is 54
 inches. How many inches is the length of the
rectangle?
width =
inches
 Length = 7 inches, Width = 9 inches
Length = 10 inches, Width = 8 inches
Length = 6 inches,  Width =8 inches
Length = 7 inches,   Width = 5 inches
The width of a rectangle is 2 inches more than
 its length. The perimeter of the rectangle is 32
inches. Select the correct length and width.
The sum of three consecutive integers is -9.
 What are the three integers? Write them in order from
least to greatest. 
The sum of three consecutive integers is 48. What
are the three integers? Write them in order from
least to greatest?
The sum of three consecutive even integers is 24.
What are the three integers? Write them below from
least to greatest.
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