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

HVAC System Operating Constraints

Explaining Compound Inequalities in Product Manufacturing