Question

At Midnight, the temp in a city was 5 degrees Celsius. The temp was dropping at a steady rate of 2 degrees Celsius per hour. Write an inequality that represents T (the number of hours past midnight) when the temp was cooler than -4 degrees Celsius. Explain or show your reasoning

Note from me: This is worth 5 points out of a 60 point math quiz so I'm suffering rn-

Answer 1

Answer: -4 > 5 - 2T

Step-by-step explanation: In the word problem, there was an initial temperature of 5 degrees. The -2T is because it drops 2 degrees per every hour after midnight. Next, you want to make the inequality T (symbol) #. Subtract 5 from both sides (-4 - 5 > -2T aka. 9 < 2T because divided by a negative which flipped the fraction). Then, divide both sides by 2 (9/2 < T or T > 9/2). To check, sub in T with a different number.

ex.

T > 9/2

5 > 9/2

☑️ true, after 5 hours, the temperature should be at -5 (less than -4)

ex.

T > 9/2

2 > 9/2

false, after 2 hours, the temperature should be at 1 (greater than -4)

Answer 2

Let's represent the temperature at any given time T hours past midnight as 5 - 2T (since it's dropping at a steady rate of 2 degrees Celsius per hour from the initial temperature of 5 degrees Celsius).

To find when the temperature is cooler than -4 degrees Celsius, set the expression 5 - 2T less than -4:

5 - 2T < -4
Now solve for T
-2T < -9

Divide both sides by -2 (note: when dividing by a negative number, the inequality sign flips):
T > 9/2

So, the inequality that represents when the temperature is cooler than -4 degrees Celsius is T > 9/2 This means the number of hours past midnight (T) must be greater then 9/2 for the temperature to be cooler than -4 degrees Celsius.