Algebra Tutorials!    
         
  Tuesday 19th of March      
 
   
Home
Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Decimals
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
Equations
   
Try the Free Math Solver or Scroll down to Tutorials!

 

 

 

 

 

 

 

 
 
 
 
 
 
 
 
 

 

 

 
 
 
 
 
 
 
 
 

Please use this form if you would like
to have this math solver on your website,
free of charge.


Graphing Linear Inequalities

Example 1

Graph the inequality x 3.

Solution

Step 1 Graph the equation that corresponds to the given inequality.

Graph the equation x = 3.

The graph is a vertical line through (3, 0).

Since the inequality symbol “” contains “equal to,” draw a solid line. The solid line shows that points on the line are solutions of the inequality.

Step 2 Use a test point NOT on the line to determine the region whose points satisfy the inequality.

The point (0, 0) is not on the line, so it can be used as a test point.

Substitute 0 for x. The resulting statement, 0 3, is false.

Therefore, the solutions do not lie in the region containing (0, 0).

The solutions lie in the other region and on the line.

Step 3 Shade the region whose points satisfy the inequality.

Since the test point (0, 0) does NOT satisfy x 3, shade the region that does NOT include (0, 0).

This is the region to the right of the solid line, including the solid line.

Note:

A vertical line divides the xy-plane into three regions:

• points on the line

• points to the right of the line

• points to the left of the line.

 

Example 2

Graph the inequality y ≥ -x.

Solution

Step 1 Graph the equation that corresponds to the given inequality.

The equation y = -x can be written as y = -1x + 0. The y-intercept is (0, 0) and the slope is -1. We use this information to graph the equation.

Since the inequality symbol “” contains “equal to,” draw a solid line to show that points on the line are solutions of the inequality.

Step 2 Use a test point NOT on the line to determine the region whose points satisfy the inequality.

The point (0, 0) is on the line, so we must select a different test point. Let’s use (2, 0).

In y -x, substitute 2 for x and 0 for y. The resulting statement, 0 ≥ -2, is true.

Therefore, the solutions lie in the region that contains (2, 0).

Step 3 Shade the region whose points satisfy the inequality.

Since the test point (2, 0) satisfies y ≥ -x, shade the region that contains (2, 0).

This is the region above the solid line, including the solid line.

Copyrights © 2005-2024