Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

NASA pilot must log at least $1000$ hours as pilot – in – command of a jet aircraft. A NASA pilot has completed all other qualification and has $250$ hours logged. How many more hours must the pilot log to become a pilot astronaut?

Write an inequality to represent the situation.
Solve the inequality. Draw the graph and check the solution.
Interpret the solutions in terms of the real – life situations.

a. The inequality of the statement is $x + 250 \geq 1000$ .

b. The solution of the inequality is $x \geq 750$ .

c. The interpretation is that the pilot should log at least $750$ hours more to become a pilot astronaut.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

a.Step -1 - Apply the concept of Linear inequalities

In this type of inequality, Simply use the property of addition or subtraction of suitable number on both Left Hand Side & Right Hand Side to maintain the inequality and also the variable & numbers should be at the different sides in the equation.

Step -2 – Find the inequality by explaining the statement

Since, the statement is pilot must log at least $1000$ hours, pilot has completed all other qualification and has $250$ hours logged.

It’s means to become a NASA pilot astronaut, a pilot must log as low as $1000$ hours.

Also, the pilot already logged $250$ hours.

Step- 3 –Make the inequality

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

So, the total hour, the pilot logged is $x + 250$

Hence, the inequality of the equation is $x + 250 \geq 1000$ .

b.Step -1 - Apply the concept of Linear inequalities

Step -2 – Find the value of x by solving the inequality

Since, the equality is $x + 250 \geq 1000$ .

Here, to simplify this inequality, subtract $250$ to both side on the above

$\begin{array}{l} x + 250 \geq 1000 \\ x + 250 - 250 \geq 1000 - 250 \\ x \geq 750 \end{array}$

Step- 3 - Check the expression to verify the inequality

Since, in the expression $x \geq 750$

So, this expression means that the value of x should be greater than or equal to $750$

So, Put $750, 751, 752, 753, . . . . . . . s o o n$ in $x + 250 \geq 1000$ to check whether the inequality hold or not

Put $x = 750$ in inequality,

$\begin{array}{l} x + 250 \geq 1000 \\ 750 + 250 \geq 1000 \\ 1000 \geq 1000 \\ 1000 = 1000 \end{array}$

It holds the equation

Again, put $x = 751$ in equality

$\begin{array}{l} x + 250 \geq 1000 \\ 751 + 250 \geq 1000 \\ 1001 \geq 1000 \end{array}$

It also holds the inequality.

So, the expression $x \geq 750$ correctly holds the inequality.

Graphical Interpretation

Following is the graph of the expression $x \geq 750$ to get the proper graphical representation to know the points.

c.Step -1 - Apply the concept of Linear inequalities

In this type of question, understand the graph carefully and make a interpretation in simple words.

Step -2 – Interpreting the solution

Since, the equality is $x + 250 \geq 1000$ .

Now, from the graph and the above inequality too, it interprets 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.

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Pre-algebra

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Short Answer

Step by Step Solution

a.Step -1 - Apply the concept of Linear inequalities

Step -2 – Find the inequality by explaining the statement

Step- 3 –Make the inequality

b.Step -1 - Apply the concept of Linear inequalities

Step -2 – Find the value of x by solving the inequality

Step- 3 - Check the expression to verify the inequality

c.Step -1 - Apply the concept of Linear inequalities

Step -2 – Interpreting the solution

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Step by Step Solution

a.Step -1 - Apply the concept of Linear inequalities

Step -2 – Find the inequality by explaining the statement

Step- 3 –Make the inequality

b.Step -1 - Apply the concept of Linear inequalities

Step -2 – Find the value of x by solving the inequality

Step- 3 - Check the expression to verify the inequality

c.Step -1 - Apply the concept of Linear inequalities

Step -2 – Interpreting the solution

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