Identify the Property
You may add the same quantity to both sides of an equation
The Addition Property of Equality
x + 3 = 7
x + 3 - 3 = 7 - 3
x = 4
Subtraction Property of Equality
x - 24 = 76
x - 24 + 24 = 76 + 24 (this line)
x = 100
Addition Property of Equality
x + 35 = 68
Subtraction Property of Equality
x = 33
x - 7 = 14
x = 21
You may subtract the same quantity from both sides of an equation
The Subtraction Property of Equality
3x = 18
3x/3 = 18/3
x = 6
The Division Property of Equality
2x - 2 = 8
2x - 2 + 2 = 8 + 2
2x = 10
2x/2 = 10/2 (This line)
x = 5
Division Property of Equality
x + 17 = 34
Subtraction Property of Equality
x = 17
9x = 72
x = 8
You may divide both sides of an equation by the same quantity
The Division Property of Equality
(1/2)x = 4
(1/2)x * 2 = 4 * 2
x = 8
The Multiplication Property of Equality
3x - 2x = 5
x = 5 (This line)
Simplification or Combining Like Terms
(1/3)x = 8
Multiplication Property of Equality;
x = 24
(1/8)x = 8
x = 64
You may multiply both sides of an equation by the same quantity
The Multiplication Property of Equality
x - 7 = 21
x - 7 + 7 = 21 + 7
x = 28
The Addition Property of Equality
8 - 2x = 4
8 - 2x - 8 = 4 - 8
-2x = -4
-2x/(-2) = -4/(-2) (This line)
x = 2
Division Property of Equality
4x - 2 = 18
(Two needed)
Addition Property of Equality and then the Division Property of Equality;
x = 5
-23 + (1/6)x = -16
x = 42
A quantity outside of a parentheses, adjacent to it, is multiplied with all items in the parentheses
The Distributive Property
3(x + 1) = 6
3x + 3 = 6
3x + 3 - 3 = 6 - 3
3x = 3
x = 1
The Distributive Property
(1/4)x - 3 + 3 = 13 + 3
(1/4)x = 16
(1/4)x * 4 = 16 * 4 (This line)
x = 64
Multiplication Property of Equality
3 - (1/2)x = 15
(Two needed)
Subtraction Property of Equality, then the Multiplication Property of Equality;
x = -24
2x - 72 + (1/2)x = 3
x = 30