SOLUTION: A car CD player has an operating temperature of |t &#8722; 44°| < 78°, where t is the temperature in degrees Fahrenheit. Express this range without using absolute value symbols.

Algebra ->  Inequalities -> SOLUTION: A car CD player has an operating temperature of |t &#8722; 44°| < 78°, where t is the temperature in degrees Fahrenheit. Express this range without using absolute value symbols.      Log On


   

Question 1122608: A car CD player has an operating temperature of |t − 44°| < 78°, where t is the temperature in degrees Fahrenheit. Express this range without using absolute value symbols.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The everyday meaning of abs%28t-44%29%3C78 is that the difference between the temperature t and 44 degrees is less than 78 degrees.

That means the temperature can be any where from 78 degrees below 44 degrees (44-78 =-34) and 78 degrees above 44 degrees (44+78 = 122). So the range of temperatures is between -34 and +122 degrees Fahrenheit.

Algebraically the inequality means that the number "t-44" is between -78 and +78:
    -78 < t-44 <  78
    +44    +44   +44
   ------------------
    -34 < t    < 122

Obviously we get the same answer either way.

It is useful to understand both methods for solving problems of this type. Depending on the particular problem where you encounter an inequality like this, one method or the other might be the easier approach.