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Q11.

Expert-verifiedFound in: Page 140

Book edition
Common Core Edition

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

Pages
183 pages

ISBN
9780547587776

**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 $x+250\ge 1000$.

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

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

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.

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.

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 $x+250\ge 1000$.

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.

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

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

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

Since, in the expression $x\ge 750$

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

So, Put $750,751,752,753,.......so\u200aon$ in $x+250\ge 1000$ to check whether the inequality hold or not

Put $x=750$ in inequality,

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

It holds the equation

Again, put $x=751$ in equality

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

It also holds the inequality.

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

**Graphical Interpretation**

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

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

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

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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