Exercise 20 Page 227

First, notice the following. 23=|n+10| ⇔ |n+10|=23 An absolute value measures an expression's distance from a midpoint on a number line. |n+10|= 23This equation means that the distance is 23, either in the positive direction or the negative direction. |n+10|= 23 ⇒ ln+10= 23 n+10= - 23 To find the solutions to the absolute value equation, we need to solve both of these cases for n.

Both n_1=13 and n_2=- 33 solve the equation.

Checking Our Answers

To check those solutions we will substitute them into the original equation. We will start with n_1=13.

We got an identity, therefore the solution is correct. Now, we will substitute n_2=- 33.

Again, we got an identity, therefore the solution is correct.