A company is making an action figure that must be at least 19.21 centimeters tall and at most 31.23 centimeters tall. How do you write a compound inequality that describes how tall the action figure can be and put the answer in set builder notation?

Question

Savannah Anderson · Accepted Answer

#H= {x : 19.21 <= x <=31.23, x in RR}#

or

#H= {x | 19.21 <= x <=31.23, x in RR}# The figure can have a length anywhere from #19.21 and 31.23#cm. These are the upper and lower limits: #19.21 <= x <=31.23# Set builder notation states that this condition must apply to all the possible values of #x# which has to be a real number. #H= {x:19.21 <= x <=31.23, x in RR}#

Hazel Anglin · Answer

undefined The compound inequality for the height of the action figure would be: $ 19.21 \leq h \leq 31.23 $, where $ h $ represents the height of the action figure.

In set builder notation, this inequality can be written as:

$$ \{ h \mid 19.21 \leq h \leq 31.23 \} $$