Chapter 1.4, Problem 50HP

To determine

To write: an absolute value equation of the given form that has no solution.

Answer to Problem 50HP

  $\left|2x-3\right|=-7x+5$

Explanation of Solution

Given information:

Given equation

  $\left|ax+b\right|=cx+d$

Assume $a,b,c$ , and $d\ne 0$ .

Calculation:

Let us take $a=2,b=-3,c=-7,d=5$ .

Now, the absolute value equation will be of the form $\left|ax+b\right|=cx+d$ and consider $x=2$ .

  $\begin{array}{c}\left|ax+b\right|=cx+d\\ \left|\left(2\right)\left(2\right)-3\right|=-7\left(2\right)+5\\ \left|4-3\right|=-14+5\\ 1=-9\end{array}$

Which is false.

Therefore, the absolute value equation $\left|2x-3\right|=-7x+5$ has no solution.