Chapter 2.2, Problem 28E

To determine

To explain:

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

  

Answer to Problem 28E

The correct inequality equation is $-10+x\ge -9$ and the number line graph of the solution $x\ge 1$ is:

  

Explanation of Solution

Given information:

  

From the image:

The main inequality equation is $-10+x\ge -9$ . On solving:

  $\begin{array}{l}-10+x\ge -9\\ -10+10+x\ge -9\\ x\ge -9\end{array}$

Now, here in the second step of above estimation there is addition of $10$ for the left side of the inequality only. It is not correct way to get solution of inequality.

So, the correct method as described as:

The given inequality equation is:

  $-10+x\ge -9$

Now, add $10$ from both sides of above equation:

  $\begin{array}{l}-10+x\ge -9\\ -10+10+x\ge -9+10\\ x\ge 1\end{array}$

So, the solution of $-10+x\ge -9$ is $x\ge 1$ . Now the number line graph of the solution $x\ge 1$ is: