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

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