Question

Write the compound inequality, or inequalities. Draw and label a number line and graph the inequalities. 8. Pilots in the U.S. Air Force must meet certain height requirements. They must be at least 5 feet 4 inches tall, but not taller than 6 feet 2 inches. Convert the heights to inches before completing the problem.

Answer 1

ANSWER and EXPLANATION

We want to write a compound inequality of the sentences given.

We have that Pilots in the US Air Force must be at least 5 feet 4 inches tall and at most 6 feet 2 inches tall.

This means that the height of the Pilots must be greater than or equal to 5 feet 4 inches and it must be less than or equal to 6 feet 2 inches.

Let us convert the heights to inches (1 foot = 12 inches):

5 feet 4 inches = (5 * 12) + 4 = 60 + 4 = 64 inches

6 feet 2 inches = (6 * 12) + 2 = 72 + 2 = 74 inches

Let the height be h, therefore:

`\begin{gathered} h\text{ }\ge\text{ 64 and h }\leq\text{ 74 inches} \\ \Rightarrow\text{ 64 }\leq\text{ h }\leq\text{ 74 } \end{gathered}`

That is the compound inequality of the sentences given.

The number line is:

That is the number line.

Now the graph:

That is the graph of the inequality.