How do you solve #|5x – 2|>= 8#?

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Answer 1 · 2016-07-17T21:51:49

#x>=2 or x<=-6/5#

If # |u(x)| >= a#. then we have:

# u(x) >= a#
or
#u(x) <=-a #

Let's apply it:

# 5x - 2 >= 8 (eq1 )#
# 5x - 2 <= -8 (eq2)#

Solving eq.1 :
# 5x >= 8 + 2#
#rArr 5x >= 10#
# rArr x >=10/5#
#rArr x >= 2#

Solving eq.2 :
# 5x - 2 <=-8#
# rArr 5x <= -8 + 2#
#rArr 5x <=-6#
#rArr x <= -6/5#

Therefore, #x>=2 or x<=-6/5#