Question

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

Answer 1

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.