absolute number question?

[Jamie27]

Find all solutions of the equation |17-n|=0.4

I believe the answer to be 16.6 or 17.4?

A) 16.6 or 17.4
B)17.4 only
C)16.6 only
D) no solution exists

if you subtrat 16.6 it does equal 0.4 but if its also negative would 17.4 work as well? I am not sure if I am going in the right direction? Thank you for any help you can offer me!

Jamie

 

[stapel]

Your reasoning is correct, and so is your answer.

Eliz.

 

[soroban]

Hello, Jamie!

Find all solutions of the equation \(\displaystyle |17\,-\,n|\: =\: 0.4\)

I believe the answer to be 16.6 or 17.4 . . . right!

Your reasoning is correct . . . Here's the algebraic approch.

Consider: \(\displaystyle |x|\,=\,3\)

This means: \(\displaystyle \,x\,=\,3\) or -\(\displaystyle 3\) . . . right?

In baby-talk: Whatever is in the absolute value equals plus-or-minus "the other side".



We have: \(\displaystyle \,|17\,-\,n|\:=\:0.4\)

This means: \(\displaystyle \,17\,-\,n\:=\:0.4\,\) or \(\displaystyle \,17\,-\,n\:=\:-0.4\)

Now solve the two equations for \(\displaystyle n\).