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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 Subtract 6x from both sides 2x + 4 +(-6x) = 6x – 12 +(-6x) Addition Property of equality 2x + (-6x) + 4 = 6x - 12 + (-6x) Move like terms together 2x + 4 +(-6x) = 6x + (-6x) -12 Commutative Property of Addition 2x + 4 + (-6x) = 6x + (-6x) - 12 Add opposites 2x + 4 + (-6x) = 0 - 12 Additive Inverse Property 2x + 4 + (-6x) = 0 - 12 Add 0 to -12 2x + 4 +(-6x) = -12 Addition/ Subtraction Property Of Zero 2x + 4 + (-6x) = - 12 Move like terms together 2x + (-6x) + 4 = - 12 Commutative Property of Addition 2x + (-6x) + 4 = - 12 Factor out the “x” [2 + (-6)] x + 4 = -12 Distributive property of Addition over Multiplication [2 + (-6)] x + 4 = -12 Add real numbers together (-4) x + 4 = -12 Substitution Property of Equality -4x + 4 = -12 Subtract 4 from both sides -4x + 4 + (-4) = -12 + (-4) Addition Property of Equality -4x + 4 + (-4) = -12 + (-4) Change order of operations by grouping - 4x + (4 - 4) = -12 + (-4) Associative Property of Addition -4x + (4 - 4) = -12 + (-4) Add opposite terms -4x + (0) = -12 + (-4) Additive Inverse Property -4x + 0 = -12 + (-4) Add zero to a number -4x = -12 + (-4) Addition Property of Zero -4x = -12 + (-4) Combine real numbers -4x = -16 Substitution Property of Equality -4x = -16 Multiply both sides by (-1/4) (-1/4) (-4x) = (-1/4) (-16) Multiplication Property of Equality (-1/4)(-4x) = (-1/4)(-16) Change order of operations by grouping (-1/4*-4)x = (-1/4 )(-16) Associative Property of Multiplication (-1/4*-4)x = -1/4 (-16) Multiply opposites 1 x = -1/4 (-16) Multiplicative Inverse Property 1x = -1/4 (-16) Multiply by 1 x = -1/4 (-16) Multiplicative Identity Property x = -1/4 (-16) Multiply real numbers together x= 4 Substitution Property of Equality 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 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