How do you write each specification as an absolute value inequality: 6.3 (is less than or equal to) h (is less than or equal to) 10.3?

1 Answer
Alan P.
Feb 10, 2017

#abs(h-8.3) <= 2#

Explanation:

Given # 6.3 <= h <= 10.3#

The midpoint between #6.3# and #10.3# is #8.3#

Remember that we can subtract the same amount for both sides of an inequality and still maintain the validity of the inequality:

#color(white)("XXX")6.3-8.3 <= h-8.3 <= 10.3 - 8.3#

#color(white)("XXX")-2 <= h-8.3 <= 2#

which we could split up as
#color(white)("XXX")-2 <= h-8.3 color(white)("X")rarrcolor(white)("X")-(h-8.3) <= 2#
and
#color(white)("XXX")h-8.3 <= 2#

which recombines as
#color(white)("XXX")abs(h-8.3) <=2#

Related questions
See all questions in Absolute Value Inequalities
Impact of this question
5570 views around the world
You can reuse this answer
Creative Commons License