Question

At midnight, the temperature in a city was 5 degrees Celsius. The temperature 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 temperature was colder than -4 degrees Celsius. Explain or show your reasoning.
On the number line, show all the values of t that make your inequality true by either submitting a picture of the drawn number line or typing a detailed description of the number line.

Answer 1

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Answer 2

SOLUTION

TO DETERMINE

At midnight, the temperature in a city was 5 degrees Celsius. The temperature 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 temperature was colder than -4 degrees Celsius.

EVALUATION

Here it is given that at midnight, the temperature in a city was 5 degrees Celsius.

The temperature was dropping at a steady rate of 2 degrees Celsius per hour.

Now t is the number of hours past midnight

So after t hours the temperature will decrease by 2t degree Celsius

So after t hours the temperature will be ( 5 - 2t ) degree Celsius

Since the temperature was colder than -4 degrees Celsius.

So the required inequality is

$\sf{5 - 2t < - 4}$

Solve for t

The obtained inequality is

$\sf{5 - 2t < - 4}$

$\implies \sf{ - 2t < - 4 - 5}$

$\implies \sf{ - 2t < - 9}$

$\implies \sf{ 2t > 9}$

$\implies \sf{ t > 4.5}$

So the required time is greater than 4.5 hours

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