Learn Before
Union of Two Inequalities
When evaluating a compound inequality connected by the word 'or', the solution consists of all numbers that make either inequality true. This combined set of solutions is the union of the two inequalities. Geometrically, if you graph each inequality on a number line, the union is the entire region formed by combining the shaded parts of both individual graphs. Just as the United States is the union of all 50 states, the mathematical solution is the union of all numbers that belong to either graph.
0
1
Tags
OpenStax
Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
Algebra
Related
Solving Compound Inequalities
Intersection of Two Inequalities
Example: Graphing the Intersection of and
Procedure for Solving Compound Inequalities with "and"
Example: Solving and Graphing and
Try It: Solving and Graphing and
Try It: Solving and Graphing and
Union of Two Inequalities
Absolute Value Inequalities with or
A quality control technician determines that a machine part is acceptable if its diameter is at least 1.95 cm and no more than 2.05 cm. This mathematical structure, which joins two distinct inequalities with a logical connector like 'and' or 'or' to define a range of solutions, is called a(n) __________.
In professional roles such as quality control or safety monitoring, mathematical constraints are often combined into a single requirement. Match each mathematical term or connector with the specific logical rule it establishes for a set of data.
In a logistics warehouse, a specialized storage unit must maintain a temperature that is greater than degrees and less than degrees to prevent spoilage. What is the mathematical term for a statement that joins two distinct inequalities with logical connectors such as 'and' or 'or' to define a specific range like this?
In professional fields such as industrial engineering and environmental safety, a 'compound inequality' is defined as a mathematical structure formed by joining two distinct inequalities with the logical connectors 'and' or 'or'.
Defining Compound Inequalities in Quality Assurance
Learn After
In a logistics warehouse, an automated sensor triggers an alarm if the internal temperature of a cold-storage unit satisfies the condition or (measured in degrees Celsius). Which mathematical term describes the combined set of all temperature values that would trigger the alarm?
A health and safety officer at a manufacturing plant is setting up an automated system that flags noise levels (in decibels) as 'unsafe' if or . Match the following mathematical components of this safety system with their correct descriptions.
In a professional quality assurance workflow, a manufacturing component is flagged for rejection if its thickness satisfies mm or mm. True or False: The mathematical term for the combined set of all thickness values that would result in a rejection is the union of the two inequalities.
In a precision manufacturing facility, a quality control sensor is programmed to flag a component if its length satisfies the condition mm or mm. To determine the union of these two mathematical conditions, a technician must identify all length measurements that make ____ of the individual inequalities true.
Defining Union in Logistics Monitoring