Question

It is currently 0 degrees outside, and the temperature is dropping 4 degrees every hour. The temperature after h hours is -4h. Explain what the equation -4h=-14 represents. What value of h makes the equation true? Explain what the inequality -4h-14 represents. What values of h make the inequality true?

Answer 1

The equation -4h = -14 represents a situation where the temperature is dropping by 4 degrees every hour, and we are trying to determine the number of hours "h" it takes until the temperature reaches -14 degrees. To solve for h, we would perform the following steps:

1. Start with the equation -4h = -14.
2. To isolate h, we want to get h by itself on one side of the equation. Since -4 is multiplied by h, we do the inverse operation which is division.
3. Divide both sides of the equation by -4:

`-4h / -4 = -14 / -4`

4. Simplify both sides:

`h = 3.5`

So the value of h that makes the equation true is 3.5, meaning it will take 3.5 hours for the temperature to drop to -14 degrees at a rate of 4 degrees per hour.

Now, let's consider the inequality -4h > -14. This inequality represents all the times (h hours) when the temperature is greater (warmer) than -14 degrees, under the same condition of the temperature dropping at 4 degrees per hour.

To solve for h in the inequality -4h > -14, we perform similar steps as we did with the equation:

1. Start with the inequality -4h > -14.
2. Divide both sides by -4, but remember that when we divide or multiply both sides of an inequality by a negative number, we have to reverse the inequality sign.

`-4h / -4 < -14 / -4`

3. Simplify both sides:

`h < 3.5`

The meaning of the inequality solution h < 3.5 is that for any time less than 3.5 hours, the temperature will be higher than -14 degrees. As time approaches 3.5 hours, the temperature will drop and exactly at 3.5 hours, it will be -14 degrees, and after that, it will become colder than -14 degrees.

Answer 2

the equation -4h=-14 represents that after h hours the temperature of the outside environment is -14°C

It means that it takes 3.5 hours for the temperature of the outside environment to be -14°C

h ≥ 3.5

Explanation:

Since the temperature after h hours is -4h, the equation -4h=-14 represents that after h hours the temperature of the outside environment is -14°C. To calculate the value of h, we divide both sides of the equation by -4.

Since -4h=-14

Dividing through by -4:

-4h / -4 = -14 / -4

h = 3.5

It means that it takes 3.5 hours for the temperature of the outside environment to be -14°C

The inequality -4h ≥ -14

Solving by dividing through by -4:

h ≥ 3.5

This means that at 3.5 hours the temperature of the outside environment must be greater than or equal to-14°C