Author: Martha Morton

Each step in solving an equation can be explained as using one of your Algebraic properties.
5x + 7 = -3
a) - 7 -7 a)
b) 5x + 0 = -10 b)
c) 5x = -10 c)
d) 5 5 d)
e) 1x = -2 e)
f) x = -2 f)
(2x + 3) + 7 = 4x + 2
a) 2x + (3 + 7) = 4x + 2 a)
b) 2x + 10 = 4x + 2 b)
c) -2x -2x____ c)
d) 0 + 10 = 2x + 2 d)
e) 10 = 2x + 2 e)
f) -2 -2 f)
g) 8 = 2x + 0 g)
h) 8 = 2x h)
i) 2 2 i)
j) 4 = 1x j)
k) 4 = x k)
l) x = 4 l)

Property	Example of Addition	Example of Multiplication
Commutative Property / The order of addition or the order of multiplication does not change the expression’s value.
Associative Property / The grouping of terms that are all being added or the grouping of terms that are all being multiplied does not change the expression’s value.
Identity Property / Adding 0 or multiplying by 1 does not change the value of an expression
Property of Equality / When using a mathematical operation on one side of an equation, it’s necessary to do the same operation on the other side of the equation to keep it balanced.
Additive/Multiplicative Inverse / The sum of two opposite values will be equal to 0. The product of 2 reciprocal values will be equal to 1.

Multiplicative Property of 0 / When a value or an expression is multiplied by 0, the product is 0.	Distributive Property of Multiplication over Addition / When an expression is being multiplied by a term or expression, each term of the expression must be multiplied.
Exponential Property of Equality / If one side of the equation has the same base as the other, the two exponents must be equal to one another	Symmetric Property / If two expressions are being compared to one another, the order of the expression on each side of the equal sign or inequality can be switched.