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	TUTORIALS:
	Absolute Values
	Solving Two-Step Equations Algebraically
	Multiplying Monomials
	Factoring Trinomials
	Solving Quadratic Equations
	Power Functions and Transformations
	Composition of Functions
	Rational Inequalities
	Equations of Lines
	Graphing Logarithmic Functions
	Elimination Using Multiplication
	Multiplying Large Numbers
	Multiplying by 11
	Graphing Absolute Value Inequalities
	Polynomials
	The Discriminant
	Reducing Numerical Fractions to Simplest Form
	Addition of Algebraic Fractions
	Graphing Inequalities in Two Variables
	Adding and Subtracting Rational Expressions with Unlike Denominators
	Multiplying Binomials
	Graphing Linear Inequalities
	Properties of Numbers and Definitions
	Factoring Trinomials
	Relatively Prime Numbers
	Point
	Inequalities
	Rotating a Hyperbola
	Writing Algebraic Expressions
	Quadratic and Power Inequalities
	Solving Quadratic Equations by Completing the Square
	BEDMAS & Fractions
	Solving Absolute Value Equations
	Writing Linear Equations in Slope-Intercept Form
	Adding and Subtracting Rational Expressions with Different Denominators
	Reducing Rational Expressions
	Solving Absolute Value Equations
	Equations of a Line - Slope-intercept form
	Adding and Subtracting Rational Expressions with Unlike Denominators
	Solving Equations with a Fractional Exponent
	Simple Trinomials as Products of Binomials
	Equivalent Fractions
	Multiplying Polynomials
	Slope
	Graphing Equations in Three Variables
	Properties of Exponents
	Graphing Linear Inequalities
	Solving Cubic Equations by Factoring
	Adding and Subtracting Fractions
	Multiplying Whole Numbers
	Straight Lines
	Solving Absolute Value Equations
	Solving Nonlinear Equations
	Factoring Polynomials by Finding the Greatest Common Factor
	Logarithms
	Algebraic Expressions Containing Radicals 1
	Addition Property of Equality
	Three special types of lines
	Quadratic Inequalities That Cannot Be Factored
	Adding and Subtracting Fractions
	Coordinate System
	Solving Equations
	Factoring Polynomials
	Solving Quadratic Equations
	Multiplying Radical Expressions
	Solving Quadratic Equations Using the Square Root Property
	The Slope of a Line
	Square Roots
	Adding Polynomials
	Arithmetic with Positive and Negative Numbers
	Solving Equations
	Powers and Roots of Complex Numbers
	Adding, Subtracting and Finding Least Common Denominators
	What the Factored Form of a Quadratic can tell you about the graph
	Plotting a Point
	Solving Equations with Variables on Each Side
	Finding the GCF of a Set of Monomials
	Completing the Square
	Solving Equations with Radicals and Exponents
	Solving Systems of Equations By Substitution
	Adding and Subtracting Rational Expressions
	Percents
	Laws of Exponents and Dividing Monomials
	Factoring Special Quadratic Polynomials
	Radicals
	Solving Quadratic Equations by Completing the Square
	Reducing Numerical Fractions to Simplest Form
	Factoring Trinomials
	Writing Decimals as Fractions
	Using the Rules of Exponents
	Evaluating the Quadratic Formula
	Rationalizing the Denominator
	Multiplication by 429
	Writing Linear Equations in Point-Slope Form
	Multiplying Radicals
	Dividing Polynomials by Monomials
	Factoring Trinomials
	Introduction to Fractions
	Square Roots

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Graphing Linear Inequalities

Helpful Hint

Why do we keep drawing graphs? When we solve 2x + 1 = 7, we donâ€™t bother to draw a graph showing 3 because the solution set is so simple. However, the solution set to a linear inequality is a very large set of ordered pairs. Graphing gives us a way to visualize the solution set.

Example 1

Inequalities with horizontal and vertical boundaries

Graph the inequalities.

a) y ≤ 5

b) x > 4

Solution

a) The line y = 5 is the horizontal line with y-intercept (0, 5). Draw a solid horizontal line and shade below it as in the figure below.

b) The points that satisfy x > 4 lie to the right of the vertical line x = 4. The solution set is shown in the following figure.

The Test Point Method

The graph of any line Ax + By = C separates the xy-plane into two regions. Every point on one side of the line satisfies the inequality Ax + By < C, and every point on the other side satisfies the inequality Ax + By > C. We can use these facts to graph an inequality by the test point method:

1. Graph the corresponding equation.

2. Choose any point not on the line.

3. Test to see whether the point satisfies the inequality.

If the point satisfies the inequality, then the solution set is the region containing the test point. If not, then the solution set is the other region. With this method, it is not necessary to solve the inequality for y.

Example 2

Using the test point method Graph the inequality 3x - 4y > 7.

Solution

First graph the equation 3x - 4y = 7 using the x-intercept and the y-intercept. If x = 0, then . If y = 0, then . Use the x-intercept and the yintercept to graph the line as shown in figure (a) below

Select a point on one side of the line, say (0, 1), to test in the inequality. Because 3(0) - 4(1) > 7 is false, the region on the other side of the line satisfies the inequality. The graph of 3x - 4y > 7 is shown in figure (b) above.