Algebra II Honors Properties Review Chapter 1

We will solve 2x + 4 = 6x – 12 Showing all of the properties used So Let’s go!

2x + 4 = 6x – 12 2x + 4 = 6x (-6x) Addition Property of equality Subtract 6x from both sides

2x + 4 +(-6x) = 6x 2x + (-6x) + 4 = 6x (-6x) + (-6x) -12 Commutative Property of Addition Move like terms together

2x (-6x) = x (-6x) = 6x + (-6x) Additive Inverse Property Add opposites

2x + 4 +(-6x) = 2x (-6x) = Addition/ Subtraction Property Of Zero Add 0 to -12

2x + = - 12 (-6x) + 4 Commutative Property of Addition 2x (-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 = (-4) Addition Property of Equality Subtract 4 from both sides

- 4x + = (-4) -4x (-4) = (-4) (4 - 4) Associative Property of Addition Change order of operations by grouping

-4x + = (-4) -4x + (4 - 4) = (-4) (0) Additive Inverse Property Add opposite terms

= (-4) -4x + 0 = (-4) -4x Addition Property of Zero Add zero to a number

-4x = x = (-4) Substitution Property of Equality Combine real numbers

(-4x) = (-16) -4x = -16 (-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 (-6x) = 6x – 12 + (-6x) 2x (-6x) = 6x + (-6x) x + 4 +(-6x) = x (-6x) = -12 2x + (-6x) + 4 = -12 [2 + (-6)] x + 4 = x + 4 = x (-4)= (-4) -4x + (4 - 4) = (-4) -4x + (0) = (-4) -4x = (-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 Step Addition Prop. of Equality Commutative Prop. of Addition Additive Inverse Property Addition Prop. of Zero Commutative Prop. of Addition Distributive Property Substitution Property Addition Property of Equality Associative Property of Addition Additive Inverse Addition Property of Zero Substitution Property Multiplication Prop. of Equality Association Prop. of Multiplication Multiplicative Inverse Multiplicative Identity Substitution