Absolute values measure distance, so that #| -x |# equals #x#. But when you try to solve for this, you have to consider that the question could be #|x|# or #|-x|# and you will get the same answer. So you need to solve for both situations

#* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *#

#5t - 2 <= 6#

*solve for #t#*

#5t <= 8#

#t < = 8/5#

#* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *#

#-(5t-2) <= 6#

#5t - 2 >= -6#

*note that the direction of the sign changed*

#5t >= -4#

#t >= -4/5#

So, we are saying that #t# is greater than #-4/5# but less than #8/5#, which you can see in this graph