Question #ecdc2

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Question #ecdc2

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Answer 1 · 2016-10-03T22:15:09

$| x - 7850 | \leq 7850$ $abs(x-7850) <= 7850$

Explanation:

$0 \leq x \leq 15700$ $0<=x <= 15700$

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

$\frac{15700 - 0}{2} = 7850$ $(15700-0)/2=7850$

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

$a a 0 a a a a a \leq x \leq a a 15700$ $color(white)(aa)0color(white)(aaaaa)<=x <=color(white)(aa) 15700$
$- 7850 a a - 7850 a - 7850$ $-7850color(white)(aa)-7850color(white)(a)-7850$

$- 7850 \leq x - 7850 \leq 7850$ $-7850<=x-7850<=7850$
or
$x - 7850 \geq - 7850, a a a a a x - 7850 \leq 7850$ $x-7850>=-7850, color(white)(aaaaa)x-7850<=7850$

Written as an absolute value, this inequality becomes

$| x - 7850 | \leq 7850$ $abs(x-7850) <= 7850$

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Question #ecdc2

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