Index Index
Absolute value, Fact
bars, Definition
formal definition, Definition
implied grouping, Item
symbol, Definition
Addition
associative property of, Paragraphs List
commutative property of, Paragraphs List
identity property of, Paragraph
inverse property of, Paragraph
of fractions with different denominators, Fact
of fractions with the same denominator, Fact
Addition method for system of linear equations. See Elimination method
Addition property
of equality, Fact
of inequality, Paragraph
Additive identity, Paragraph
Additive inverse, Paragraph
Algebraic expression, Paragraph
evaluating, Example
simplifying, Example
Algebraic expressions
simplifying, Paragraph
Algebraic translations of English phrases, Paragraph
Associative property, Paragraphs
of addition, List
of multiplication, List
Axis
horizontal, Definition
vertical, Definition
Cartesian coordinate system, Paragraph Definition
René Descartes, Section
Combining like terms, Subsection Paragraphs
Common denominator, Fact
Commutative property, Paragraphs
of addition, List
of multiplication, List
Coordinate plane, Definition
Coordinates, Definition
of a point, Section
Denominator, Paragraphs
adding and subtracting fractions with different, Fact
adding and subtracting fractions with the same, Fact
common, Fact
least common, Fact
Dependent equations, Paragraph
Dependent system, Paragraph
Distributive property, Paragraphs List
Division property of equality, Fact
Elimination method
for system of linear equations, Subsection
systems having infinitely many solutions, Example
systems having no solution, Example
English phrases and sentences
algebraic translations of, Paragraph
Equation
linear, Definition
Equation of a line
horizontal line, Paragraph
point-slope form, Definition
slope-intercept form, Definition
standard form, Definition
vertical line, Example
Equation(s), Paragraph
addition property of equality for solving, Fact
dependent, Paragraph
equivalent, Paragraph
inconsistent, Paragraph
multiplication property of equality for solving, Fact
solution of, Definition
solution set of, Paragraph
translating to, Paragraph
using both addition and multiplication properties, Subsection Process
with fractions, Paragraph
Equations in two variables
graphing, Paragraph
linear, Definition
Equivalent equations, Paragraph
Evaluating algebraic expressions, Example
Exponent
implied grouping, Item
Expression
algebraic, Paragraph
linear, Paragraph
Factors, Paragraph
Formulas, Paragraph
Fraction
adding and subtracting with the different denominators, Fact
adding and subtracting with the same denominator, Fact
clearing denominators, Paragraph
common denominator, Fact
denominator, Paragraphs
implied grouping, Item
improper, Subsection
linear equations with, Paragraph
mixed number, Paragraph
multiplication, Fact
numerator, Paragraphs
reducing, Subsection
Graph
of an equation, Paragraph
of an inequality, Example
Graphing
equations in two variables, Paragraph
intercepts, Example
linear equations in two variables, Paragraph
lines in slope-intercept form, Figure
solution set to an inequality, Example
systems of linear equations, Subsection
Graphs
of inequalities, Figure
Greater-than symbol, Paragraph
Greater-than-or-equal-to symbol, Paragraph
Grouping symbol, Item
Identity, Subsection
additive, Paragraph
multiplicative, Paragraph
Identity property
of addition, Paragraph
of multiplication, Paragraph
Improper fraction, Subsection
Inconsistent equations, Paragraph
Inconsistent system, Paragraph
Inequalities, Paragraph
graphing, Example
solution sets of, Example
solutions of, Definition
with infinitely many solutions, Example
with no solutions, Example
Inequality
linear, Definition
Integers, Item
Intercept, Paragraph Subsection
graphing, Paragraph
Intercepts
finding, Example
Interval notation, Definition
Inverse
additive, Paragraph
multiplicative, Paragraph
Inverse property
of addition, Paragraph
of multiplication, Paragraph
Irrational numbers, Item
Least common denominator (LCD), Fact
Less-than symbol, Paragraph
Less-than-or-equal-to symbol, Paragraph
Like radicals, Item
Like terms, Paragraph
Linear equations, Definition
intercepts used for graphing, Subsection
solving, Subsection Process
with fractions, Paragraph
with infinitely many solutions, Example
with no solution, Example
Linear equations in one variable, Definition
Linear equations in two variables, Definition
graphing, Paragraph
Linear expression, Paragraph
Linear inequalities, Definition
solving, Subsection Process
Linear inequalities in one variable, Paragraph Definition
Linear system of equations, Definition
Lines
slope of, Definition
Mathematical models, Section
Mixed numbers, Paragraph
Mixture problems, Example
Modeling, Section
Multiplication
associative property of, List
commutative property of, List
explicit, Remark
identity property of, Paragraph
implicit, Remark
inverse property of, Paragraph
of fractions, Fact
Multiplication property
negative, Fact
Multiplication property of equality, Fact
Multiplicative identity, Paragraph
Multiplicative inverse, Paragraph
Natural numbers, Item
Negation property of equality, Paragraph
Negative multiplication property of inequality, Fact
Negative numbers, Paragraph
Negative reciprocals, Fact
Negative signs and parentheses, Paragraph
Negative slope, Item
Not-equal-to symbol, Paragraph
Number line, Paragraph
Numerator, Paragraphs
Opposite, Paragraph
Order of operations, List
Ordered pair, Section Definition
as solution of equation, Paragraph
as solution of linear system, Definition
Origin, Definition
Parallel lines, Fact
and slope, Fact
Percent, Paragraph
applications, Subsection
Percent symbol, Paragraph
Perfect squares, Paragraph
Perpendicular lines, Fact
and slope, Fact
Plotting points, Paragraph
Point-slope form, Definition
Points
plotting, Paragraph
Positive numbers, Paragraph
Positive slope, Item
Problem solving
with substitution method, Subsection
Proportions, Paragraph
applications of, Example
Quadrant, Definition
Radical, Paragraph
implied grouping, Item
Radical symbol, Paragraph
Radicals
like, Item
Rate, Paragraph
Rate of change, Subsection Definition
Rational numbers, Item
as decimals, Item Subsection
Real numbers, Item
absolute value of, Definition
ordering, Checkpoint
negative, Fact
Rectangular coordinate system, Paragraph
finding coordinates of points, Section
Reduced fraction, Subsection
Reducing a fraction, Subsection
Relationship
constant, Paragraph
Repeating decimal, Item
Rise over run, Remark
Satisfy an equation, Paragraph
Satisfy an inequality, Paragraph
Set, Paragraph
empty, Warning
Set-builder notation, Definition
Signed numbers, Subsection
adding, Subsection
multiplying, Subsection
raised to powers, Subsection
subtracting, Subsection
Simplifying a fraction, Subsection
Simplifying algebraic expressions, Example Checkpoint
Slope, Definition
and parallel lines, Fact
and perpendicular lines, Fact
as rate of change, Definition
definition, Definition
formula, Example
given intercepts, Fact
negative, Item
of a line, Definition
positive, Item
triangle, Example
undefined, Fact
zero, Item
Slope-intercept form, Definition
graphing lines in, Figure
Solution mixture problems, Example
Solution set
of equation, Paragraph
of inequality, Example
Solution(s)
of an inequality, Definition
of equations, Definition
of equations in two variables, Section
of system of linear equations, Definition
Solving
linear equations
multistep, Process
linear inequalities
multistep, Process
Solving an equation, Paragraph
Solving an inequality, Paragraph
Square root, Paragraph
Square root sign, Paragraph
Standard form, Definition
problem solving with, Example Subsection Example
Substitution of number for variable, Example
Subtraction
translating phrases, Paragraph
Subtraction property of equality, Fact
Symbol
grouping, Item
percent, Paragraph
radical, Paragraph
Systems of linear equations, Definition
applications, Example Checkpoint Example Subsection Example Example Example Example
solved by elimination, Subsection Process
solved by graphing, Subsection
with infinitely many solutions, Subsection Example Example
with no solution, Subsection Example Example
Systems of two linear equations
number of solutions, List
Terminating decimal, Item
Terms, Definition
like, Paragraph
of algebraic expressions, Definition
Types of numbers
integers, Item
irrational, Item
natural, Item
rational, Item
real, Item
whole, Item
Undefined
slope, Fact
