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

Jan 1, 2018

75

#### Explanation:

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

$2 | x - 5 | < 16$

$| x - 5 | < 8$

$x - 5 < 8 \setminus \rightarrow x < 13$
$x - 5 > - 8 \setminus \rightarrow x > - 3$

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

These numbers sum to 75.