SOLUTION: I am trying to find the solution for the following inequality containing absolute values: |7-x| <6 Thank you.

Algebra ->  Absolute-value -> SOLUTION: I am trying to find the solution for the following inequality containing absolute values: |7-x| <6 Thank you.      Log On


   



Question 269423: I am trying to find the solution for the following inequality containing absolute values:
|7-x| <6
Thank you.

Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is the problem:
(i) +abs%287-x%29+%3C+6
we have to split and solve:
first 7-x < 6
second 7-x > - 6
---
step 1 - solve first equation to get
(ii) 7-x+%3C+6
step 2 - subtract 7 to get
(iii) -+x+%3C+-1
step 3 - divide by -1 to get
(iv) x+%3E+1
---
step 4 - solve second equation to get
(v) 7-x+%3E+-6
step 2 - subtract 7 to get
(vi) -+x+%3E+-13
step 3 - divide by -1 to get
(vii) x+%3C+13
----
so
1 < x < 13.