Algebra I
Variable -> a letter used to stand for a number
When you use a letter to stand for a number, you don’t know what number that letter
represents.
Mathematical expressions are named based on how many terms they have.
 A monomial expression has one term. x is a monomial expression
 A binomial expression has 2 unlike terms combined by an addition or subtraction sign.
o x + 3 is a binomial expression.
 A trinomial expression has 3 unlike terms combined by addition and/or subtraction signs.
 A polynomial expression has 2, 3 or more unlike terms combined by addition and/or
subtraction signs.
Such as -> x+y+z-4
A mathematical sentence contains 2 mathematical phrases joined by an equals sign or an
inequality sign. When you see ≠ it means not equal to.
An equation is a mathematical sentence in which 2 phrases are joined by an equals sign.
3 + 6 = 9 is an equation.
Some equations are true and some are false.
 3 = 1 + 2 is a true equation.
 3 + 5 = 7 is an equation, but it is false. Therefore should be written as 3 + 5 ≠ 7
Whether an equation is true, false, or open depends on the value of the variable.
An inequality is a mathematical sentence in which 2 phrases are joined by an inequality symbol.
The inequality symbols are
 greater than, “>”
 greater than or equal to, “>”
 less than “<”
 less than or equal to “<”
In mathematics there are 4 basic operations, addition, subtraction, multiplication and division.
A number and a variable are unlike terms.
 7 and x are unlike terms.
Terms that use different variables are unlike terms.
 3z, b, and -2x are unlike terms.
Just like you can add numbers, you can add variables, provided their variables are the same.
 3x + 7x = 10x
33
1
 4x + 12x – ½x = 16x - ½x = 𝑥 = 15 𝑥
2


2
You cannot simplify 3x + 5y because the variables are not the same.
You cannot simplify 3x + 4 because 3x is a variable expression and 4 is a number.
When you see a variable 7x
7 = the coefficient and x = variable
Subtraction is the same. You can subtract 1 number from another. You can subtract like terms.
*When subtracting expressions with the same variables, just subtract the co-efficients &
attach the variable to the new coefficient. Do not subtract the variables.
5x -3x ≠2
5x-3x =2x
Multiplication A centered dot indicates multiply.
3 ∙ 5 = 15
7b = 7 ∙ b
6(2) = 12
You can multiply any 2 variables
x ∙ y =xy
a ∙ b = ab
y ∙ y = y2
You can multiply a number & a variable
3 ∙ x = 3x
You can multiply a number and a variable with a coefficient
3 ∙ 5x = 15x
You can multiply 2 expressions each of which have numbers and variables
3x ∙ 2y = 6xy
4x ∙ 5x = 20x2
Division –
You can divide any 2 numbers.
21 ÷ 7 = 3
You can divide 2 of the same variables.
You can divide different variables.
x/x = 1
a/b
You can divide 2 different numbers with 2 different variables. 8x / 2y = 4
𝑥
𝑦