Intersection and Union in Absolute Value Inequalities
Let us understand how we can take Intersection and Union in Absolute Value Inequalities.
Union of Inequalities
For a given set of values, if the inequality is x>=a or x<b then we need to find the union of the values of x which can be given by
Case 1: x >= a or x < b
{x: x < b U x ≥ a}
Case 2: x < a or x >= b
{x: x <a U x ≥ b} = {x: x < a}∪{x: x ≥ b}.
The solution i.e. the union can be calculated using graph. Consider the example x <= 3 || x >= -4 , then the union of the inequalities will give an overlapping interval which will include all real numbers as shown below.
Union of Inequalities
Intersection of Inequalities
For a given set of values, if the inequality is x >= a and x < b then we need to find the intersection of the values of x which can be given by
Case 1: a <= x < b
{x: a≤x < b}
Case 2: a <= x U b > x
{x: a ≤ x U x < b}
The solution i.e. the intersection can be calculated using graph. Consider the example x <= 4 U x >= -5 , then the intersection of the inequalities will give an interval which will include all real numbers from -5 and 4 as shown below.
Intersection of Inequalities
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Absolute Value Inequalities
Inequalities that involve algebraic expressions with absolute value symbols and inequality symbols are called Absolute Value Inequality. In this article, we will discuss inequalities and absolute value inequalities and others in detail.
Table of Content
- What is Inequalities?
- What is Absolute Value Inequalities?
- Solving Absolute Value Inequalities
- Types of Absolute Value Inequalities
- Intersection and Union in Absolute Value Inequalities
- Examples on Absolute Value Inequalities
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