Chapter 1.4, Problem 49E

To determine

To Identify:

Correct the error in given equation.

Answer to Problem 49E

Error is it made a wrong conclusion, as $x=4,x=5$ is a false statement.

Explanation of Solution

Given information:

  $\left|2x-1\right|=-9$

Solution $=-4,5$

Calculation:

For converting the given sentence as an inequality, consider the variables and numbers that go o the left hand side and right hand side.

For identifying the type of inequality should be used.

Given equation is,

  $\begin{array}{l}\left|2x-1\right|=-9\\ 2x-1=-9\\ 2x=-8\\ x=4\end{array}$

And

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

Here error is it made a wrong conclusion.

As $x=4,x=5$ is a false statement $x=4,x=5$ is not in a solution set of the inequality.

The error is it made a wrong conclusion, as $x=4,x=5$ is a false statement.