Linear Inequalities – JSS2 Mathematics Lesson Note (Second Term)

 Linear inequalities

Inequality is an algebraic expression formed by replacing the equal sign of an equation with an inequality symbol. e.g. 7X + 5 = 16 (equation while 5X + 7 > 9 (inequality).

The following are commonly used in an inequality symbol. 

V

Symbol meaning representation

< LESS THAN

>  GREATER THAN

≤ LESS THAN OR EQUAL TO

≥ GREATER THAN OR EQUAL TO

 We often use inequality in our everyday life. We can write them as algebraic statements. For example, if the speed of a car is 250km/h or less, we can write this as S ≤ 250, where s represents speed.

Graph of inequalities

A linear inequality has no square or higher power of the unknown. In other words, the power of the unknown is 1.

Example 1: 2x > 15 is a linear inequality in one variable. (X).

Solution:

2X > 10 [divide both sides by 2

2X/2 > 10/2

X = 5.

                                      1    2    3    4     5    6    7    8   

The empty circle at the end of the arrow shows that 5 is not included in the range

Combining inequalities

When combining inequalities (sometimes an unknown quantity obeys more than one inequality), these inequalities may be combined as one statement, the smallest number must be written first followed by the unknown, and finally the largest number, and vice-versa. For example, the diagram below shows that X can take any value from -2 to 3.

                                           -6   -5   -4     -3     -2     -1     0     1     2     3    4

Hence the inequalities are X ≥ -2 and X < 3

But X ≥ -2 in reverse is written as a ≤ X and X < 3 can be combined as a single inequality as follows

-2 ≤ X ≤ 3.

Example 1:                                          

 -6  -5  -4   -3   -2    -1   0    1    2    3    4     5    6                                                    

             X ≥ -1,     X ≤ 5

-1 ≤ x ≤ 5

Example 2:

      -5    -4    -3    -2    -1    0    1    2  

X > -5, X ≤ 2

-5 < X ≤ 2