Question

THERMOMETER An outdoor thermometer claims to be accurate within

2 degrees Fahrenheit. One day, the thermometer reads 72°F.
a. Write an absolute value inequality that represents the possible actual
temperature t.
b. What is the range of possible actual temperatures?

Answer 1

a. An absolute value inequality that represents the possible actual temperature t is:

|t - 72| < 2

b. To find the range of possible actual temperatures, we can solve the inequality:

|t - 72| < 2

We can split this into two separate inequalities, one for when t is greater than 72 and one for when t is less than 72:

t - 72 < 2 and -(t - 72) < 2

Simplifying these inequalities, we get:

t < 74 and t > 70

Therefore, the range of possible actual temperatures is 70°F < t < 74°F.

Step-by-step explanation:

Answer 2

To represent the possible actual temperature t, use the absolute value inequality |72 - t| < 2. The range of possible actual temperatures is 70°F < t < 74°F.

Step-by-step explanation:

a. To represent the possible actual temperature t, we can use the absolute value inequality: |72 - t| < 2. This means that the difference between the thermometer reading (72°F) and the actual temperature (t) should be less than 2 degrees.

b. The range of possible actual temperatures can be determined by solving the inequality. Subtracting 72 from both sides of the inequality gives: -2 < t - 72 < 2. Adding 72 to all terms gives: 70 < t < 74. Therefore, the range of possible actual temperatures is 70°F < t < 74°F.