Chapter 1.4, Problem 49E

To determine

To describe and correct the error in solving the equation,

Explanation of Solution

Given information:

Given equation

  $\begin{array}{l}\left|2x-1\right|=-9\\ 2x-1=-9or2x-1=-\left(-9\right)\\ 2x=-82x=10\\ x=-4x=5\end{array}$

The solutions are $x=-4$ and $x=-5$

Calculation:

Consider the equation $\left|2x-1\right|=-9$ .

The steps for the above linear equation are given as follows.

  $\begin{array}{c}2x-1=-9or2x-1=-\left(-9\right)\\ 2x=-8or2x=10\text{Add}1\text{on}\text{both}\text{sides}\\ x=-4orx=5\text{Divide}\text{by}2\text{on}\text{bothsides}\end{array}$

The value is negative 9 in the given equation which indicates that the absolute value is negative number. This is not true and the given equation has no solution. It should not be solve as shown in the above steps. This is the error made.