Question

Question #ecdc2

Answer 1

`abs(x-7850) <= 7850`

Explanation:

`0<=x <= 15700`

`0` and `15700` are the endpoints of an interval. Find the middle of the interval by subtracting 0 from 15700 and dividing the result by 2.

`(15700-0)/2=7850`

Then write the inequality in terms of `-7850` and `7850`.

`color(white)(aa)0color(white)(aaaaa)<=x <=color(white)(aa) 15700`
`-7850color(white)(aa)-7850color(white)(a)-7850`

`-7850<=x-7850<=7850`
or
`x-7850>=-7850, color(white)(aaaaa)x-7850<=7850`

Written as an absolute value, this inequality becomes

`abs(x-7850) <= 7850`