Graph for Inequalities
Inequalities are either with one variable or two or we have a system of inequalities, all of them can be graphed to the cartesian plane if it only contains two variables. Inequalities in one variable are plotted on real lines and two variables are plotted on the cartesian plane.
Interval Notation for Inequalities
Important points for writing intervals for inequalities:
- In case of greater than and equal to (≥) or less than equal to (≤), the end values are included so, closed or square brackets [ ] are used.
- In case of greater than (>) or less than (<), the end values are excluded so, open brackets () are used.
- For both positive and negative infinity open brackets () are used.
The following table represents intervals for different inequalities:
Inequality |
Interval |
---|---|
x > a |
(a, ∞) |
x < a |
(-∞, a) |
x ≥ a |
[a, ∞) |
x ≤ a |
(-∞, a] |
a < x ≤ b |
(a, b] |
Graph for Linear Inequalities with One Variable
From the following table we can understand, how to plot various Linear Inequalities with One Variable on a real line.
Inequality |
Interval |
Graph |
---|---|---|
x > 1 |
(1, ∞) |
|
x < 1 |
(-∞, 1) |
|
x ≥ 1 |
[1, ∞) |
|
x ≤ 1 |
(-∞, 1] |
Graph for Linear Inequalities with Two Variable
Let’s take an example of linear inequalities with two variables.
Consider the linear inequality 20x + 10y ≤ 60, as the possible solutions for given inequality are (0, 0), (0,1), (0, 2), (0,3), (0,4), (0,5), (0,6), (1,0), (1,1), (1,2), (1,3), (1,4), (2,0), (2,1), (2,2), (3,0), and also all the points beyond these points are also the solution of the inequality.
Let’s plot the graph from the given solutions.
The shaded region in the graph represents the possible solutions for the given inequality.
Also Read
Inequalities
Inequalities are the expressions which define the relation between two values which are not equal. i.e., one side can be greater or smaller than the other. Inequalities are mathematical expressions in which both sides are not equal. They are used to compare two values or expressions. It is a mathematical expression used to compare the relative size or order of two objects or values.
They are fundamental in solving problems in mathematics, economics, engineering, and various other fields.
In this article, we will learn about Inequalities including their symbols, rules/properties, types, and their graphical representations and others in detail.