How do you solve # abs(2 - 5x )>= 2 / 3#?
1 Answer
Explanation:
You're dealing with an absolute value inequality, so right from the start, you should know that you must look at two possible cases
#2 - 5x >= 0 implies |2 - 5x| = 2 - 5x# In this case, you have
#2 - 5x >= 2/3# This will get you
#-5x >= 2/3 - 2#
#-5x >= -4/3 implies x <= 4/15#
#2 - 5x < 0 implies |2 - 5x| = - (2 - 5x)# In this case, you have
#-2 + 5x >= 2/3# This will get you
#5x >= 2/3 + 2#
#5x >= 8/3 implies x >= 8/15#
You can thus say that the solution interval for the original inequality will be
#x in (-oo, 4/15] uu [8/15, + oo)#
This tells you that the original inequality is satisfied if
#x in (4/15, 8/15)#
is not a solution to the original inequality.