Chapter 1.4, Problem 12E

To determine

To solve the equation:

  $\left|r\right|=-2$

And also graph the solution.

Answer to Problem 12E

No solution.

Explanation of Solution

Given:

  $\left|r\right|=-2$

Concept Used:

To solve $\left|ax+b\right|=c,c\ge 0$ , solve the related equations:

  $ax+b=c,\text{ or }ax+b=-c$

When $c<0$ the absolute value equation $\left|ax+b\right|=c$ has no solution, since absolute value always indicates a value that is not negative.

Calculation:

In order to solve the equation:

  $\left|r\right|=-2$

Note that $-2<0$ , and the absolute value always indicates a value that is not negative. So, there is no value of r that satisfies the equation

Thus, the equation $\left|r\right|=-2$ has no solution.