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Boundless Algebra
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Algebra

Chapter 2

Introduction to Equations, Inequalities, and Graphing

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
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Section 1
Variables and Expressions
Introduction to Variables

Variables are useful in mathematics for many reasons, and can be used to denote different types of arbitrary or unknown numbers.

Adding and Subtracting Algebraic Expressions

Simplifying algebraic expressions may require one to follow some key steps to add and subtract like terms.

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Multiplying Algebraic Expressions

The process for multiplying algebraic expressions differs for monomials and polynomials.

Simplifying Radical Expressions

Radical expressions containing variables can be simplified to a basic expression in a similar way to those involving only integers.

Simplifying Exponential Expressions

The rules for operating on numbers with exponents can be applied to variables with exponents as well.

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Rational Algebraic Expressions

The addition and subtraction of rational expressions are bound by all of the same rules as the addition and subtraction of fractions.

Section 2
Introduction to Equations
What is an Equation?

Equations with variables have solutions, or values for the variables that make the statements true.

Solving Equations: Addition and Multiplication Properties of Equality

The addition and multiplication properties of equalities are common ways used to solve equations.

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Rational Equations

A rational equation sets two rational expressions equal to each other and involves unknown values that make the equation true.

Radical Equations

Equations involving radicals are often solved by moving the radical to one side of the equation and then squaring both sides.

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Equations with Absolute Value

To solve an equation with an absolute value, first isolate the absolute value, and then solve for the positive and negative cases.

Section 3
Inequalities
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Introduction to Inequalities

Inequalities are used to demonstrate relationships between numbers or expressions.

Rules for Solving Inequalities

Operations can be conducted on inequalities and used to solve inequalities for all possible values of a variable.

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Compound Inequalities

A compound inequality involves three expressions, not two, but can also be solved to find the possible values for a variable.

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Inequalities with Absolute Value

Inequalities with absolute values can be solved by thinking about absolute value as a number's distance from 0 on the number line.

Section 4
Graphing and Equations of Two Variables
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The Cartesian System

The Cartesian coordinate system is used to visualize points on a graph by showing the points' distances from two axes.

Equations in Two Variables

Equations in two variables represent the relationship between two variables and have a series of solutions.

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Graphing Equations

Equations and their relationships can be visualized in many different types of graphs.

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Graphs of Equations as Graphs of Solutions

A solution to an equation can be plotted on graphs to better visualize how the equation, or function, behaves.

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Graphing Inequalities

The solutions to inequalities can be graphed by drawing a boundary line to divide the coordinate plane in two and shading in one of those parts.

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Boundless Algebra by Boundless
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Chapter 1
Numbers and Operations
  • Introduction to Arithmetic Operations
  • Properties of Real Numbers
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  • Radicals
  • Further Exponents
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Chapter 2
Introduction to Equations, Inequalities, and Graphing
  • Variables and Expressions
  • Introduction to Equations
  • Inequalities
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Chapter 3
Systems of Equations
  • Systems of Equations in Two Variables
  • Systems of Equations in Three Variables
  • Systems of Inequalities and Linear Programming
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