Inequalities

Basic Rules of Inequalities

 

Solving

Our aim is to have x (or whatever the variable is) on its own on the left of the inequality sign:

Example: 

We called that "SOLVED"

How to Solve?

 

Safe things to do: 

These are things we can do without affecting the direction of the inequality:

1. Add (or subtract) a number from both sides
2. Multiply (or divide) both sides by a positive number

 

Adding or Subtracting a Value

 

What did we do?

What If I Solve It, But "x" Is On The Right?

No matter, just swap sides, but reverse the sign so it still "points at" the correct value!

 

Multiplying or Dividing by a Value

Positive Values

Everything is fine if we want to multiply or divide by a positive number:

  

Negative Values

When we multiply or divide by a negative number, we must reverse the inequality.

Let us try an example:

 

Just remember, When multiplying or dividing by a negative number, reverse the inequality!

 

Multiplying or Dividing by Variables

Example 01:

 

To help you understand, imagine replacing b with 1 or -1 in that example:

• if b is 1, then the answer is simply x < 3
• but if b is -1, then we would be solving -x < -3, and the answer would be x > 3

Example 02:

 

NOW, Two Inequalities At Once!

 

 

 

Now, Let's try some exercises!

 

 References:

http://www.mathsisfun.com/algebra/inequality-solving.html