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Intersection of Two Inequalities
When evaluating a compound inequality connected by the word "and", the solution consists of all numbers that make both inequalities true simultaneously. This shared set of solutions is known as the intersection of the two inequalities. Geometrically, if you graph each inequality on a number line, the intersection is the specific region where the shaded parts of both graphs overlap.
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Intermediate Algebra @ OpenStax
Ch.2 Solving Linear Equations - Intermediate Algebra @ OpenStax
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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
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Compound Inequalities with No Solution
A quality control technician at a manufacturing plant is testing the length () of a precision component. The component is only acceptable if its length is greater than 10.5 mm AND less than 10.7 mm. Which mathematical term specifically describes the set of all values that satisfy both conditions at the same time, represented by the overlap of their individual graphs on a number line?
An environmental safety officer is monitoring the pH level of a local stream to ensure it is healthy for aquatic life. The stream is considered safe only if the pH satisfies the condition that it is greater than 6.0 AND less than 8.5. The mathematical term for the shared set of values that satisfy both of these conditions simultaneously, represented by the overlap of their individual graphs on a number line, is the __________ of the two inequalities.
An HVAC technician is monitoring the pressure () in a boiler system. To operate safely, the pressure must be greater than psi AND less than psi. Match each term or visual concept below with its correct description regarding the set of safe pressure values.
A quality control inspector at a bottling plant is checking the volume () of liquid in a container. The container passes inspection only if is greater than mL AND less than mL. The mathematical term 'intersection' describes the solution set containing all values that satisfy both of these conditions simultaneously.
Vaccine Storage Temperature Requirements