How do you solve the inequality #abs(4-1/2x)<=6#?

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Answer 1 · 2017-05-02T11:12:30

#-4 <= x <= 20#

#-6 <= 4 - 1/2 x <= 6#

Subtract four

#-10 <= - 1/2 x <= 2#

Multiply by #-2#

#20 >= x >= -4#

Answer 2 · 2017-05-02T11:19:27

Solution: #-4<=x<=20#. In interval notation: #[-4 , 20]#

# | 4-1/2x| <= 6 or 4-1/2x <= 6 or -1/2x <= 6-4 or -x <= 2*2 or x >= -4 # OR

# | 4-1/2x| <= 6 or 4-1/2x >= -6 or -1/2x >= -6-4 or -x >= -10*2 or x <= 20 #

Solution: #-4<=x<=20#. In interval notation: #[-4 , 20]# [Ans]