Inequations
Statements such as
x < 3, 2x + 1 < 5, 3x – 1 > 8, 3 – 5x > 2
are called inequations.
In general, a inequation in the variable x can be written in one of the forms :
(i) ax + b < 0
(ii) ax + b < 0
(iii) ax + b > 0
(iv) ax + b > 0
where a, b are fractions, a ? 0
Solving Linear Inequations in One Variable
Solving linear inequations in one variable
The rules for solving linear inequations are similar to those for solving equations except for multiplying or dividing by a negative number.
We can do any of the following to an inequation :
• add the same number or expression to both sides
• subtract the same number or expression from both sides
• multiply both sides by the same positive number
• divide both sides by the same positive number
However, when we multiply or divide by the same negative number, the inequation changes direction
Representing Inequations on a Number Line
Every inequation can be representing on a number line. See the following examples:
Example. Represent x < 3, x ? N, on the number line
Solution. Given x < 3, x ? N,
The solution set = 1, 2
The solution set is shown by thick dots on the number line.
Example. Represent the inequality – 3 < x < 5, x ? I, graphically.
Solution. Given – 3 < x < 5, x ? I
The solution set = - 2, - 1, 0, , 1, 2, 3, 4, 5
The solution set is shown by thick dots on the number line
Example.
Represent x < 3, x ? N,
Solution.
Given x < 3, x ? N
The solution set = 1, 2
Example.
Represent the inequality – 3 < x < 5, x ? I,
Solution.
The solution set = - 2, -1, 0, 1, 2, 3, 4, 5
Related Tags
inequation , inequation problems , inequation examples