1. Expressions and Equations

2. A symbol or letter that represents one or more numbers.
- Normally a letter

3. A number multiplied by a variable or product of variables
- a number next to a variable

4. constants A number on its own in an expression or equation. Example
Definition
constants
Characteristics
Non-Example
- A number

5. A mathematical phrase that can have a contain numbers, variables, and operators.
Does not have an equal sign
Contains +, -, x, and/or ÷

6. Algebraic Expressions
Examples:

7. To solve algebraic equations, you need
to isolate the variable. Perform the inverse operation.
The inverse of addition is
subtraction.
The inverse of subtraction is
addition.
The inverse of division is
multiplication.
The inverse of multiplication is
division.
Remember: whatever you do to
one side, you must do to the
other!

8. The product of a number and a sum is the same as the product of individual addends and the number.
Has both multiplication and addition or subtraction
Has paratheses

9. Two or more terms that have the same variables raised to the same powers.
The variables in a term must be the same
The exponents with the variables must be the same

10. 3, 24, -1/2, 0.75
3 & -9y
24 & 7a²
2x & 3x, 4y & -9y,
7a² & 2a²
2a² & 2x
2x+3x = 5x, 4y-9y=-5y,
7a² + 2a² = 9a²
5a³ & 9a²
Constants with constants
Same variable with same exponent
Add or subtract the coefficients
Cannot combine constants with variables and different exponents

11. Examples:
4a – 3b + 7a
16b – 4x + 3b + 14x
-4m + 8b – 4c + 13c
(4a + 3b + 8r)- (3a + 10b + 6r)
(15g + 4b) + (11g + 13b) + (8g + 13b)

15. Distributive Property
Find the sum. -2x + 3x
Look for common factors. X
Rewrite the expression. (-2 · x) + (3 · x)
Take out the common factor. X(-2 + 3)
Simplify = 1 x(1) = x -2x + 3x = x
Find the sum. ( 2 3 x x)
Use the number properties. Associative
( x x) = 0
Simplify. Additive Inverses and Identity Property
2 3 x + 0 = 2 3 x ( 2 3 x x) = 2 3 x

16. Distributive Property
Factor each expression completely. 12n –
Look for the GCF (variables too!) n
Use the distributive property. (12 · n) – ( 3 8 m · n)
Take out the GCF and put in front of the ( ). n( )
The rest goes inside the ( ). n( m )
3 8 mn

17. Two-Step Equations
3x + 15 = 18
1. Get rid of the constant by using the inverse of addition or subtraction.
16 – 4x = 64
2. Isolate the variable by using the inverse of multiplication or division.
3(4m – 5) = -19
*Check your answer!
5𝑥 2 = 10

18. Solving Inequalities
Solve inequalities just like you would solve an equation. BUT……
*When multiplying or dividing inequalities with a negative number, you need to FLIP the sign!
1. Isolate the variable and divide by the factor. *Do not forget the negative!*
1. Divide by the inverse.
2. Reverse the inequality sign.
2. Flip the inequality sign.
-40x > -30
−𝑥 3 > 8
By a negative number
Dividing both sides
By a negative number
Multiplying both sides

19. Graphing Inequalities
𝑠 3 >3
f + 7 < 2
open
V – 8 ≥ 1
𝑝 2 ≤3
closed
*The direction of the graph will be the same as your final answer of your inequality sign.
−𝑥 3 >8