Algebra II Honors

Properties Review

Chapter 1

We will solve2x + 4 = 6x – 12

Showing all of the properties used

So Let’s go!

2x + 4 = 6x – 12

2x + 4 = 6x - 12

+(-6x) +(-6x)

Addition Property of equality

Subtract 6x from both sides

2x + 4 +(-6x) = 6x

2x + (-6x) + 4 = 6x - 12 + (-6x)

+ (-6x) -12

Commutative Property of Addition

Move like terms together

2x + 4 + (-6x) = - 12

2x + 4 + (-6x) = 6x + (-6x) - 12

0

Additive Inverse Property

Add opposites

2x + 4 +(-6x) =

2x + 4 + (-6x) = 0 - 12

-12

Addition/ Subtraction PropertyOf Zero

Add 0 to -12

2x + = - 12(-6x) + 4

Commutative Property of Addition

2x + 4 + (-6x) = - 12

Move like terms together

+ 4 = -12

2x + (-6x) + 4 = - 12

[2 + (-6)] x

Distributive property of Addition over Multiplication

Factor out the “x”

x + 4 = -12

[2 + (-6)] x + 4 = -12

(-4)

Substitution Property of Equality

Add real numbers together

-4x + 4 = -12

-4x + 4 = -12

+ (-4) + (-4)

Addition Property of Equality

Subtract 4 from both sides

- 4x + = -12 + (-4)

-4x + 4 + (-4) = -12 + (-4)

(4 - 4)

Associative Property of Addition

Change order of operations by grouping

-4x + = -12 + (-4)

-4x + (4 - 4) = -12 + (-4)

(0)

Additive Inverse Property

Add opposite terms

= -12 + (-4)

-4x + 0 = -12 + (-4)

-4x

Addition Property of Zero

Add zero to a number

-4x = -16

-4x = -12 + (-4)

Substitution Property of Equality

Combine real numbers

(-4x) = (-16)

-4x = -16

(-1/4) (-1/4)

Multiplication Property of Equality

Multiply both sides by (-1/4)

= (-1/4 )(-16)

(-1/4)(-4x) = (-1/4)(-16)

(-1/4*-4)x

Associative Property of Multiplication

Change order of operations by grouping

x = -1/4 (-16)

(-1/4*-4)x = -1/4 (-16)

1

Multiplicative Inverse Property

Multiply opposites

= -1/4 (-16)

1x = -1/4 (-16)

x

Multiplicative Identity Property

Multiply by 1

x =

x = -1/4 (-16)

4

Substitution Property of Equality

Multiply real numbers together

2x + 4 = 6x – 12 2x + 4 + (-6x) = 6x – 12 + (-6x) 2x + 4 + (-6x) = 6x + (-6x) - 12

2x + 4 +(-6x) = 0 - 12 2x + 4 + (-6x) = -12 2x + (-6x) + 4 = -12 [2 + (-6)] x + 4 = -12

-4x + 4 = -12 -4x + 4 + (-4)= -12 + (-4)-4x + (4 - 4) = -12 + (-4)

-4x + (0) = -12 + (-4)-4x = -12 + (-4)

-4x = -16(-1/4) (-4x) = (-1/4 )(-16)(-1/4*-4)x = (-1/4) (-16)

1x = -1/4 (-16)x = -1/4 (-16)

x= 4

Properties Step by StepAddition Prop. of Equality Commutative Prop. of Addition Additive Inverse Property Addition Prop. of ZeroCommutative Prop. of AdditionDistributive PropertySubstitution PropertyAddition Property of EqualityAssociative Property of AdditionAdditive InverseAddition Property of ZeroSubstitution PropertyMultiplication Prop. of EqualityAssociation Prop. of MultiplicationMultiplicative InverseMultiplicative IdentitySubstitution