Chapter 1.4, Problem 32E

To determine

Towrite:Anabsolute value equation that has the given solutions.

Answer to Problem 32E

The required absolute equation is $|x-8|=2$ .

Explanation of Solution

Given information:

The given solutions are $x=-6$ and $x=10$ .

Formulaused:

The value of absolute equation $|x-a|=b$ is $|x-a|=b$ are $x=b-a$ and $x=b+a$ .

Calculations:

Let given equation be $|x-a|=b$ . So, its solution are $x=b-a$ and $x=b+a$ . But the given solutions are $x=-6$ and $x=10$ . Therefore, we have

  $b-a=-6$.... (1)

  $b+a=10$.... (2)

Adding results (1) and (2)

  $2b=4$

  $\Rightarrow b=\frac{4}{2}=2$

Substituting value of b in result (1)

  $2-a=-6$

  $\Rightarrow a=2+6$

  $\Rightarrow a=8$

Now, $|x-a|=b\Rightarrow |x-8|=2$

Thus, the required absolute equation is $|x-8|=2$ .

Conclusion:

The required absolute equation is $|x-8|=2$ .