Axioms
Distributive /Factoring
Solving Equations
Properties
Wild
100
x = x
Reflexive Axiom of Equality
100
Factor out the common factors: 5x2 - 25xy
5x(x - 5y)
100
9x - 3 - 8x = 7
x = 10
100
Give the reason for statement 2.
1. (1/2)x = 30
2. (2)(1/2)x = (2)(30)
Muliplication property of equality
100
What property was used to transform the following equation?
3x - 7 = 29
= 3x - 7 +7 = 29 + 7
Additive Property of Equality
200
x ∙ (1/x) = 1
multiplicative inverse axiom
200
Simplify: 5 - 3(9 - 7x)
-22 + 21x or 21x - 22
200
3(a + 2) = 18
a = 4
200
Give the reason for statement 2.
1. 3x + 5 = 20
2. 3x +5 + (-5) = 20 + (-5)
Additive Property of Equality
200
Give the reason for this statement:
9x - 1 = 9x + (-1)
Definition of Subtraction
300
(xy)z = x(yz)
Associative axiom of multiplication
300
Factor out the common factors: 2x - 12y + 22z
2(x - 6y + 11z)
300
6(x + 2) - 4x = 48
x = 18
300
Give the reason for the statement.
12 ∙ (-1) = -12
Multiplicative property of (-1)
300
Solve for x AND specify the numerical coefficient of the variable in your answer.
4x + 3 = 2x + 9
3x
numerical coefficient = 3
400
x(y + z) = xy + xz
Distributive axiom of multiplication over addition
400
Simplify: 3/2(8 + 12x)
12 + 18x
400
(4 + 12) + (x + 4) = (3 ∙ 4) + 8
x = 0
400
Give the reason for the statement.
12 ∙ 0 ∙ x = 0
Multiplicative property of zero
400
6/2 = 6 ∙ (1/2)
Definition of division
500
If x = y and y = z, then x = z
Transitive axiom of equality
500
Factor out the common factors: 9ax2 + 81a2x
9ax(x +9a)
500
6x + 3(x + 7) = -15
x = -4
500
Give the reason for the bottom statement.
Muliplication property of equality
500
DOUBLE POINTS!
Give the first step to proving that the following expression is equal to 3.5 + x: (include the statement and reason)
= 4/2 + 2/2x + 3/2
Distributive axiom of division over addition