How do you solve and write the following in interval notation: #− 1/2 ≤ (4 − 3x) / 5 ≤ 1/4#?

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Answer 1 · 2017-07-21T11:49:01

Solution: # 11/12 <=x <= 26/12# , in interval notation: # [11/12,26/12]#

# -1/2 <= (4-3x)/5 <= 1/4 # (multiplying by #20#)

# -10 <= 4(4-3x) <= 5 # or

#-10 <= 16-12x) <= 5 # (adding #-16#)

#-26 <= -12x <= -11 # (dividing by #12#)

#-26/12 <= -x <= -11/12 # (multiplying by #-1#)

#26/12 >= x >= 11/12 or 11/12 <=x <= 26/12#

Solution: # 11/12 <=x <= 26/12# , in interval notation # [11/12,26/12]# [Ans]