Inequality Notation

Inequalities are algebraic equations and it variable x cannot be equal. Inequalities have the different values. In general, inequality notation is used to describe intervals. The inequality notations are,

Greater than

Less than

= Greater than or equal to

= Less than or equal to

The inequality also has chained inequality notation abc which means ab and bc.

Inequality Notation Properties:

The inequality notation “a  b" is read as "a is less than b"
The inequality notation "a  b" is read as "a is greater than b"


These notations define as the sense of the inequality.

(a) If the signs of inequality point in the same direction the same logic is used

(b) If the signs of inequality point in the opposite direction then it is opposite logic/sense.

Inequality Notation for intervals:

Example:

Use inequality notation to illustrate each set.

All the Y in the interval (-4, 8)
X is nonnegative


Solution:

The inequality notation is,

-4  y  8,

0  x

Example problems on inequality:

Example 1:

Solve the inequality 4x+ 2  3

Solution:

4x+ 2  3

Subtract 2 from both sides

4x+2 -2  3-2

4x  1

Divide both sides by 4

4x/4  1/4

x1/4

This means that ANY number greater than ¼ will make the equation 4x+ 2  3 true!

Example 2:

Solve the inequality y + 12  24

Solution:
Simply subtract 12 from each sides:

y + 12 -12   24 -12

y  12


This means that ANY number less than 12 will make the equation y + 12  24 true!

Examples 3:

Solve the inequality       x-35 and 2x+14 16

Solution:

Step 1: Solve the first inequality

X-35

Add 3 on both sides,

x-3 + 3 5+3

x8

Step 2: solve the second inequality

2x+14 16

Subtract 14 from both sides,

2x+14-14  16 -14

2x12

Divide by 2 on both sides

x6

The final solution is: x8 and x6

This means that 6x8.