How do you solve #-2|4x+1|<-6#?

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Answer 1 · 2016-11-12T19:03:23

#x< -1 or x > 1/2#

# -2 |4x +1| < -6#

Divide both sides by -2 and reverse the inequality

#hArr | 4x + 1 | > 3 #

The modulus can be written in two inequalities.

# hArr 4x + 1 <-3 #

# or 4x + 1 > 3 #

Solving the first inequality
#hArr 4x + 1 < -3 #

#hArr 4x < -4#

#hArr x < -1#

Solving the second inequality

#hArr 4x + 1 > 3#

#hArr 4x > 2#

#hArr x > 1/2#