1. Properties of Equality and Solving One-Step Equations

2. Vocabulary Property In symbols In words Reflexive property of equality
a = a
A number is equal to itself.
Symmetric property
If a = b, then b = a.
If numbers are equal, they will still be equal if the order is changed.
Transitive property
If a = b and b = c, then a = c.
If numbers are equal to the same number, then they are equal to each other.
Substitution
property of equality
If a = b, then b may be
substituted for a in any
expression containing a.
If two numbers are equal, then
substituting one in for another does not change the equality of the equation.

3. Property
In symbols
In words
Addition property
of equality
If a = b, then a + c = b + c.
Adding the same number to both sides of an equation does not change the equality of the equation.
Subtraction
property of equality
If a = b, then 
a – c = b – c.
Subtracting the same number from both sides of an equation does not change the equality of the equation.
Multiplication
If a = b and 
c ≠ 0, then
a • c = b • c.
Multiplying both sides of the equation by the same number, other than 0, does not change the equality of the equation.
Division property
c ≠ 0, then 
a ÷ c = b ÷ c.
Dividing both sides of the equation by
the same number, other than 0, does not change the equality of the equation.

4. Property General rule Specific example
Commutative property
a + b = b + a
a • b = b • a
3 + 8 = 8 + 3
3 • 8 = 8 • 3
Associative property
(a + b) + c = a + (b + c)
(a • b) • c = a • (b • c)
(3 + 8) + 2 = 3 + (8 + 2)
(3 • 8) • 2 = 3 • (8 • 2)
Distributive property
a • (b + c) = a • b + a • c
3 • (8 + 2) = 3 • • 2

5. Like Terms
Like terms have the same variable or combination of variables, and those variables have the same exponents.
Ex. 3 𝑥 2 𝑦 𝑎𝑛𝑑 18 𝑥 2 𝑦
𝑥 𝑎𝑛𝑑 15𝑥

6. Combining Like Terms 2x To combine like terms add the coefficients.
Example.
4𝑥+3𝑥−6𝑥 2x
variable

7. Example
Given: 2x - 4y - 3x + 7y Combine like terms.

8. Example
Given: 3 𝑥 2 +9 𝑦 4 −10 𝑥 2 − 𝑦 Combine like terms

9. Solving Equations
Solving an equation for a variable means finding the values of the variable that make the equation true.
To do this we must isolate the variable to one side of the equation by using inverse operations.

10. Inverse Operations
Inverse operations undo operations; you can think of them as opposites.
-Addition and subtraction are inverse operations.
-Multiplication and division are inverse operations.

11. An equation is like a balance scale because it shows that two quantities are equal.
What you do to one side of the equation must also be done to the other side to keep it balanced.

12. Example
Given: k + 5 = 17 solve for k.

13. Example
Given: 2x = 18 solve for x.

14. Example
Given: 9 + x = 20 solve for x.