What the sum of the integer solutions of the compound inequality #2abs(x-5)#<16#?

1 Answer
Jan 1, 2018

Answer:

75

Explanation:

First let's see if we can solve the inequality:

#2|x-5|<16#

#|x-5|<8#

#x-5<8\rightarrow x <13#
#x-5 > -8\rightarrow x > -3#

This gives the compound inequality: #-3 < x < 13#
Since we only want integer solutions, we're looking at the numbers:
#{-2,-1,0,1,2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12}#

These numbers sum to 75.