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Algebra (Intermediate) - Inequalities
 
Symbols | Solving Inequalities
 

Symbols

The symbols for inequalities are as follows:

 Greater than  ›
 Less than  ‹
 Greater than or equal to  ≥
 Less than or equal to  ≤

 
Solving Inequalities

We can solve inequalities in the same way as we solved equations.

Example 1:
Solve
2y + 3 > 15
 (–3)


2y > 12
   (divide by 2)
 
y > 6  
    

y > 6 is the solution, showing that the following are possible integer values of y: 7, 8, 9, 10, ..................


Example 2:
Solve
3y – 6 ≤ 9  
 ( + 6)


3y ≤ 15
   (÷ 3)
 
y ≤ 5  
    

In this case we include 5 in the solution because of the ≤ sign.

The possible integer values of y are: 5,6,7,8,9,..........

If the term in y is negative, always move it to the other side and make it positive, as in the following example.


Example 3:

Solve
5 – 2y > 3       

 

(+ 2y)


        5 > 3 + 2y

 

 

 
        2 > 2y

 

(divide by 2 )

 
        1 > y
    

We read an inequality from the letter side so this reads 'y is less than 1' (y<1)

The possible values of y are 0, –1, –2, –3,...........

Note what to do if two inequality signs are used, as in the following case.


Example 4:

Solve
3x – 1 > 2x < x + 5
    

In this instance, we split them up.

      
 
3x – 1 > 2x
and
2x < x + 5
  
 
3x – 2x >1   
  
2x – x < 5      
  
 
x >1   
  
x < 5      
  
 
The possible values of x are 2, 3, 4.

The solution to an inequality is called 'the range of values'.

Inequalities can be plotted graphically. (See the study note on graphs).