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Example of linear inequalities; y ≤ x – 1 and y < –2x + 1
A combination of linear inequality equations with the same variables is referred to as a system of linear inequalities.
There are five inequality symbols used to represent equations of inequality.
These are less than (<), greater than (>), less than or equal (≤), greater than or equal (≥), and the not equal symbol (≠). Inequalities are used to compare numbers and determine the range or ranges of values that satisfy the conditions of a given variable.
Example of linear inequalities;
Graph the following system of linear inequalities:
y ≤ x – 1 and y < –2x + 1
Graph the first inequality y ≤ x − 1.
We will draw a solid border and shade below the line due to the "less than or equal to" mark.
On the same x-y axis, graph the second inequality, y -2x + 1.
In this instance, the less-than symbol will cause our boundaries to be dashed or dotted. Under the border, cast a shade.
As a result, the darker-colored zone extending indefinitely downward is the solution to this inequality problem, as seen below.
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