Rearrange: |x-5|<c into x>=5-c, where c>0?

Part of a maths question on continuity. I just cant seem to see how to do it. btw the %26gt;= sign is greater than or equal to, i couldn't find the actual symbol on character map

Rearrange: |x-5|%26lt;c into x%26gt;=5-c, where c%26gt;0?
this is | x - 5 | %26lt; c c %26gt; 0 so





-c %26lt; x- 5 %26lt; c





add 5 on all the terms





-c + 5 %26lt; x %26lt; c + 5





so x %26gt; 5- c and %26lt; 5+ c





x= 5-c is not correct as when x = 5-c |x -5| = |-c| = c which is not the given condition


x %26gt; 5+ c is not correct as x %26gt;5+c means x-5 %26gt; c so |x -5| %26gt; c not correct
Reply:|x-5|%26lt;c is equivalent to


-c%26lt;x-5%26lt;c


Solve for x,


5-c%26lt;x%26lt;5+c
Reply:|x-5|%26lt;c


-c %26lt; x-5 %26lt; c


-c+5 %26lt; x %26lt; c+5


5-c %26lt; x %26lt; c+5





So x %26gt; 5-c but not equal to it.
Reply:(x-5)%26lt;c


therefore x%26lt;c+5 as 5 has been added to both sides