Home
Math by Grades Pre-K
Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grades 7 and 8
Grades 9 and 10
Grades 11 and 12
Math by Topics Arithmetic
Algebra
Geometry
Math Word Problems
Trigonometry
Statistics
Probability
PreCalculus
Calculus
Set Theory
Matrices
Vectors
Math Worksheets Math Worksheets
Interactive Zone
Math in Video Lessons Basic Algebra
Intermediate Algebra
College Algebra
High School Geometry
College Calculus
Linear Algebra
Engineering Math
Singapore Math
Math for Specific Tests SAT Math
ACT Math
GMAT Math
High School, Regents
California Standards
GCSE Maths
A Level Maths
Math Fun and Games Math Trivia
Math Games
Fun Games
Mousehunt Guide
Exam Preparation SAT Preparation
ACT Preparation
GMAT Preparation
Science Biology
Chemistry
Science Projects
High School Biology
High School Chemistry
High School Physics
GCSE Biology
Others English Help
ESL, IELTS, TOEFL
Programming
Animal Facts
Tutoring Services
What's New

 

Systems of Linear Inequalities

We can solve systems of linear inequalities either algebraically or graphically.

 

 

Solving Systems of Linear Inequalities Algebraically

When solving systems of linear inequalities (or simultaneous inequalities):
Step 1: Solve each inequality separately
Step 2: Find the common values between the two inequalities. (Use a number line if necessary)

Example:

Solve the following simultaneous inequalities and represent your solution set on the number line.
x + 2 < 6 and x – 3 > – 1

Solution:
x + 2 < 6
x < 6 – 2
x < 4

x – 3 > – 1
x > – 1 + 3
x > 2

Common values: 2 < x < 4

 

 

 

Example:

Find the integer values of x satisfying the simultaneous inequality:
6 < 2 – 3x < 14

Solution:
Write 6 < 2 – 3x < 14 as two separate inequalities and solve them separately.
  6 < 2 – 3x
 3x < 2 – 6
 3x < – 4
   x <

2 – 3x < 14
   – 3x < 14 – 2
   – 3x < 12
      3x > –12
        x > – 4
Common values: – 4 < x <

The integer values of x are  –3 and –2

 

 

Solving System of Linear Inequalities Graphically

We can also solve systems of linear inequalites graphically. The following videos show some examples of solving systems of linear inequalites graphically

 

 

 

Custom Search

 

We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.

 

© Copyright 2005, 2009 - onlinemathlearning.com
Embedded content, if any, are copyrights of their respective owners.

Useful Links:
More Algebra Help at MathWorld
 

 

 

Custom Search