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Systems of Linear Inequalities




 
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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 inequalities graphically. The following videos show some examples of solving systems of linear inequalities graphically



 


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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