Chapter 3.4, Problem 11E

To determine

To write an inequality which represent the situation, solve and graph the solution of the inequalities.

Answer to Problem 11E

The inequality equation is obtained as $x+250\le 1000$ .

Explanation of Solution

Given information:

To become a NASA pilot astronaut, a pilot must log at least 1000 hours as pilot-in-command.

The pilot already logged 250 hours.

Calculation:

Let, $x$ be the remaining hours which a pilot must logged to become NASA pilot astronaut.

Since, the pilot already logged 250 hours.

So, total hours, the pilot logged is $x+250$ .

And, to become a NASA pilot astronaut, a pilot must log at least 1000 hours as pilot-in-command.

Hence,

The inequality equation is obtained as:

  $x+250\ge 1000$

Solve the inequality,

Subtract $250$ to both sides

  $\begin{array}{l}x+250\ge 1000\\ x+250-250\ge 1000-250\left[\text{Subtract 250 from both sides}\right]\\ x\ge 750\left[\text{Simplify}\right]\end{array}$

The solution is $x\ge 750$ .

The graph is obtained as:

  

To check the solution, choose any number less than or equal to 750. Substitute the number into the original inequality.

  $\begin{array}{l}x+250\ge 1000\\ 900+250\ge 1000\left[\text{Substitute 900 for }x\right]\\ 1150\le 1000\left[\text{Solution checks}\right]\end{array}$

Interpretation:

From, the above graph, it can be interpreted that the pilot should log at least 750 more hours as pilot in command of a jet aircraft to become a pilot astronaut as the pilot already logged 250 hours.