Chapter 1, Problem 15CT

To determine

To explain:

An extraneous solution of $\left|4x+20\right|=6x$ is $x=-2$ without calculation

Answer to Problem 15CT

An absolute value equation is never being negative, so $x=-2$ is an extraneous solution for $\left|4x+20\right|=6x$ .

Explanation of Solution

Given information:

  $\left|4x+20\right|=6x$

Calculation:

Now, the given equation is:

  $\left|4x+20\right|=6x$

… (1)

Put the $x=-2$ in the right hand side of the above equation, get that:

  $\begin{array}{l}6x=6\left(-2\right)\\ 6x=-12\end{array}$

That means; the right hand side of the eq. (1) rewrite as:

  $\begin{array}{l}\left|4x+20\right|=6x\\ \left|4x+20\right|=-12\end{array}$

Now, the result of an absolute value equation is never being negative. That’s why $x=-2$ is an extraneous solution.