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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#