Chapter 3.5, Problem 28E

To determine

To Describe and Correct:The error in solving the inequality $9x>-45$ .

Answer to Problem 28E

The final answer is $x>\text{ -5}$

Explanation of Solution

Given information:The inequality $9x>-45$ is solved incorrectly. To do the error analysis of the calculations given below.

  $\begin{array}{l}\Rightarrow 9x>\text{ -45}\\ \Rightarrow \frac{9x}{9}<\frac{-45}{9}\\ \Rightarrow x<\text{ -5}\end{array}$

Formula used: The Division Property of Inequality is used.

  $\begin{array}{l}\text{If }a<b\text{ and }c>0\text{, then }\frac{a}{c}<\frac{b}{c}\\ \text{If }a<b\text{ and }c<0\text{, then }\frac{a}{c}>\frac{b}{c}\end{array}$

Calculation:

The given inequality expression is,

  $\Rightarrow$ $9x>-45$

Divide both sides with $9$

  $\Rightarrow \frac{9x}{9}>\frac{-45}{9}$

As $9>0$ , the direction of the inequality symbol will not be reversed.

On doing division, the inequality becomes,

  $\Rightarrow x>-5$

Thus, the correct answer is $x>-5$ .