The Algebra Pyramid

Handouts            Intermediate Algebra

EQUATIONS AND INEQUALITIES
Equations and Inequalities are SOLVED

An equation is made up of two expressions
that are set equal   =   to each other 

An equation in one variable has a finite number of solutions (the same number as its degree)

Set notation is not used to write the solutions.
Solutions are written in the form
variable = constant

 An inequality is made up of two expressions separated by an inequality symbol  <     <     >   or   >  

An inequality in one variable has an infinite number of solutions (a set of them)

Set notation is used to write the solutions.
Solutions are written in set-builder notation.

 

*EXPRESSIONS
Expressions are SIMPLIFIED
(by following order of operations)
*An expression is a meaningful collection of constants, variables and arithmetic symbols (operation symbols).
Terms are to be added
(they are separated by + or – symbols)
(subtraction is addition of the opposite)
Factors are to be multiplied
(division is multiplication by the reciprocal)

CONSTANTS, VARIABLES
(there are no operations that can be performed)
A constant is a number.                         
A variable is a letter used to represent a number
A term is a number or a variable or a number times a variable;
the variable may or may not have an exponent
A monomial is a polynomial with only one term

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