Chapter 2.2, Problem 35E

To determine

To explain:

The solution set of $x-11\ge -3$ and numbers used to verify inequality solution

Answer to Problem 35E

The solution set of $x-11\ge -3$ is $x\ge 8$ and numbers used to verify inequality solution is $8$ or greater than $8$ .

Explanation of Solution

Given information:

  $x-11\ge -3$

As per the problem’s condition, it is not possible to check all numbers given in the solution set for the inequality equation. It is not possible because the inequality equation ranges from negative infinity to certain constant or from certain constant to positive infinity.

For the inequality equation $x-11\ge -3$ , on solving:

Add $11$ on both sides of eqns:

  $\begin{array}{l}x-11\ge -3\\ x-11+11\ge -3+11\\ x\ge 8\end{array}$

So, to check and verify the solution of inequality equation $x-11\ge -3$ , the numbers are inequality equation $8$ or greater than $8$ should be used.