Solving Compound Inequalities

Intersection of Two Inequalities

Example: Graphing the Intersection of $x > -3$ and $x \leq 2$

Procedure for Solving Compound Inequalities with "and"

Example: Solving and Graphing $6x - 3 < 9$ and $2x + 9 \geq 3$

Try It: Solving and Graphing $4x - 7 < 9$ and $5x + 8 \geq 3$

Try It: Solving and Graphing $3x - 4 < 5$ and $4x + 9 \geq 1$

Union of Two Inequalities

Absolute Value Inequalities with $<$ or $\leq$

A quality control technician determines that a machine part is acceptable if its diameter $d$ 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 ${}35$ degrees and less than ${}45$ 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