Chapter 1.4, Problem 31E

To determine

To find:The absolute value equation.

Answer to Problem 31E

Here, the absolute value equationis $|x-13|=5$ .

Explanation of Solution

Given: $x=8$ and $x=18$

Calculation:

To find what the variable is subtracted by, find the number that is halfway between the two solutions. In this case, $13$ is half way between $8$ and $18$ .

  $|x-13|$

To find that the absolute equation is set to equal to, find the difference between one value of $x$ and what it is being subtracted by. $8-13=-5$ and $18-13=5$ . So, the equation is set to $5$ .

  $|x-13|=5$

Conclusion:

Therefore, the absolute value equationis $|x-13|=5$ .