Chapter 1: Equations and Inequalities

variable

variable

symbols, usually letters, that represent unknowns (i.e

algebraic expression

an expression that contains at least one variable (i.e

order of operations

used to solve expressions and equations, used to solve for variables

Step 1

evaluate expressions inside grouping symbols

Step 2

evaluate all powers

Step 3

multiply and/or divide from left to right

Step 4

add and/or subtract from left to right

monomial

an algebraic expression that is composed of a number, a variable, or the product of a number and a variable (i.e

constants

monomials that contain no variables (i.e

coefficient

the numerical part of a monomial with a variable (i.e

degree

the sum of the exponents of the variables in a monomial (i.e

polynomial

a monomial OR a sum of monomials

terms

the monomials that make up a polynomial (i.e

like terms

terms that can be combined (i.e

trinomial

three unlike terms (i.e

x^2 + 3x

1, none of the terms can be combined)

binomial

two unlike terms (i.e

formula for the area (A) of a trapezoid

A = 1/2 h(b1 + b2), where h is the height, and b1 and b2 are the lengths of the bases

variable

symbols, usually letters, that represent unknowns

algebraic expression

an expression that contains at least one variable

order of operations

used to solve expressions and equations, used to solve for variables

monomial

an algebraic expression that is composed of a number, a variable, or the product of a number and a variable

constants

monomials that contain no variables

coefficient

the numerical part of a monomial with a variable

degree

the sum of the exponents of the variables in a monomial

power

an expression with the form x^n - also used to refer to the exponent itself

polynomial

a monomial OR a sum of monomials

terms

the monomials that make up a polynomial

like terms

terms that can be combined

trinomial

three unlike terms

binomial

two unlike terms

formula

a mathematical sentence that expresses the relationship between certain quantities

real numbers

numbers that correspond to exactly one point on the number line, every point represents

rational numbers

a number that can be expressed as a ratio, where the numerator and denominator are integers, and the denominator is NOT zero

irrational numbers

a number that cannot be expressed as a ratio

open sentence

a mathematical sentence with one or more variables

equation

a mathematical sentence that sets two expressions equal to each other

solution

whenever a variable is replaced by a number

absolute value

the distance of a number from 0 on a number line, represented by |x|

empty set

solution set of an equation with no solution set

compound inequality

two inequalities joined by the word and or the word or

intersection

the set of elements common to two sets, the graph of a compound inequality containing and

union

the set of elements belonging to one or more of a group of sets, the graph of a compound inequality containing or