The temperature, t, in degrees Fahrenheit, in a certain town on a certain spring day

The temperature, t, in degrees Fahrenheit, in a certain town on a certain spring day satisfies the inequality ⎪t - 24⎪ ≤ 30. Which of the following temperatures, in degrees Fahrenheit, is NOT in this range?

  1. -10
  2. -6
  3. -5
  4. 0
  5. 54

Answer

The correct answer is A.

⎪t - 24⎪ ≤ 30

It means that the distance on the number line between t and 24 is at most 30 units. This distance would be greater than 30 only when t was more than 30 above 24 or more than 30 below 24. That is when t is more than 54, or t is less than -6.

t - 24 ≤ 30 or t - 24 ≥ -30

t ≤ 54 or t ≥ -6

So, -6 ≤ t ≤ 54