This preview shows page 1. Sign up to view the full content.
Unformatted text preview: oblems and solving the
two linear equations. x  2 =  ( 3 x + 1) = 3 x  1 x  2 = 3x + 1 or  2x = 3 or 4x = 1
1
x=
4 or x= 3
2 Okay, we’ve got two potential answers here. There is a problem with the second one however. If
we plug this one into the equation we get,
?
3
æ 3ö
  2 = 3ç  ÷ +1
2
è 2ø  7? 7
=2
2
7
7
¹2
2 NOT OK We get the same number on each side but with opposite signs. This will happen on occasion
when we solve this kind of equation with absolute values. Note that we really didn’t need to plug
the solution into the whole equation here. All we needed to do was check the portion without the
absolute value and if it was negative then the potential solution will NOT in fact be a solution and
if it’s positive or zero it will be solution.
We’ll leave it to you to verify that the first potential solution does in fact work and so there is a
single solution to this equation : x = 1
and notice that this is less than 2 (as our assumption
4 required) and so is a solution to the equation with the absolute value in it.
So, all together there is a single solution to this equation : x = 1
.
4
[Return to Problems] (...
View
Full
Document
 Spring '12
 MrVinh

Click to edit the document details