Question

Explain how compound inequalities are used in medicine.

Short answer

The explanation for the compound inequalities are used in medicine is shown in the below steps.

Step-by-step solution

Step 1. Write definition.

A compound inequality is a sentences with two inequality statements joined either by the word “or” or by the word “and”.

Here the word “and” indicates that both statements of the compound sentences are true at the same time. It is the overlap or intersection of the solution sets for the individual statements.

The word “or” indicates that, as long as either statements is true, the entire compound sentence is true. It is the combination or union of the solution sets for the individual statements.

Step 2. Write the inequalities in another way.

Given inequalities,

$h\ge 10$ and $h\le 16$

This can be written as in the following way.

$10\le h\le 16$

Step 3. Write an example.

Suppose a patient is diabetic and requires insulin is a glucose tolerance test. Patient start the test in a fasting state means they have had no food or drink except water for at least 8 hours but no more than 12 hours.

So, the acceptable number of hours h for fasting can be described by the following compound inequality.

$h\ge 8$ and $h\le 12$

Step 4. Sketch the graph.

The graph of $h\ge 8$ and $h\le 12$ sketch in below.