Write an absolute value inequality that represents an interval in which to estimate t. Solve inequality and interpret answer

Question

A refrigerator manufacturer recommends that the temperature inside the refrigerator be 37 degrees Fahrenheit. Let t represent temperature. If the thermostat has a margin of error of no more than 1 degree.

Answer 1

36 < t < 38

set the thermostat at 37 degrees and it may actually be anywhere from 36 to 38 degrees, given a margin of error of 1 degree

|t -37| < 1

is the equivalent of -1 < t-37 < 1,

add 37 to the left, middle and right to get 37-1 < t-37+37 < 1 +37 equivalent to 36 <t< 38

the absolute value of (the actual temperature minus 37) is less than or equal to 1, the margin of error

or

the absolute value of the difference between 37 and the temperature is less than or equal to 1

You'll probably find a page or two on the topic "Inequalities Involving Absolute value" in most college algebra textbooks, giving some examples and how to solve them.