# 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 **or** greater than or equal to

#x in (4/15, 8/15)#

is **not** a solution to the original inequality.