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Answer 1 · 2016-10-03T22:15:09

$abs(x-7850) <= 7850$

$0<=x <= 15700$

$0$ 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

$abs(x-7850) <= 7850$