Chapter 2.2, Problem 27E

To determine

To explain:

The correct equation for the following inequalities equation or its graphing solution:

  

Answer to Problem 27E

The correct inequality equation is $x-14>-17$ and the number line graph of the solution $x>-3$ is:

  

Explanation of Solution

Given information:

  

From the image:

The main inequality equation is $-17<x-14$ . on solving:

  $\begin{array}{l}-17<x-14\\ -17+14<x-14+14\\ -3<x\end{array}$

Now, here in the second step of above estimation there is no sides switching is done. Only addition of number and then solve the inequality

But the correct method is first switch sides and then estimates its solution.

So, switch the sides of $-17<x-14$ as:

  $\begin{array}{l}-17<x-14\\ x-14>-17\end{array}$

Now, add $14$ from both sides of above equation:

  $\begin{array}{l}x-14>-17\\ x-14+14>-17+14\\ x>-3\end{array}$

So, the solution of $x-14>-17$ is $x>-3$ . Now the number line graph of the solution $x>-3$ is: