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Zorluk: OrtaSolving Linear Inequalities

A warehouse is cooling a refrigerated storage room. The initial temperature of the room is 22∘C22^\circ\text{C}. A cooling system lowers the temperature by 1.8∘C1.8^\circ\text{C} per hour. To store a specific vaccine, the temperature of the room must be kept strictly below −5∘C-5^\circ\text{C}. What is the minimum number of whole hours the cooling system must run to reach a safe storage temperature?

Cevap: 16 hours

Cevap

The minimum number of whole hours the cooling system must run is 16.
To find the minimum number of whole hours, we set up the inequality 22−1.8h<−522 - 1.8h < -5. Subtracting 22 from both sides yields −1.8h<−27-1.8h < -27. Dividing by the negative rate −1.8-1.8 requires reversing the inequality sign, which gives h>15h > 15. The smallest integer greater than 15 is 16.

Adım Adım Çözüm

1
Set up the inequality representing the temperature condition.
22−1.8h<−522 - 1.8h < -5
The initial temperature is 22∘C22^\circ\text{C}, and it decreases by 1.8∘C1.8^\circ\text{C} per hour hh. The temperature must be strictly below −5∘C-5^\circ\text{C}.
2
Isolate the variable term by subtracting 22 from both sides.
−1.8h<−27-1.8h < -27
Subtracting 22 simplifies the left side and groups the constant terms on the right side.
3
Divide both sides by -1.8 and reverse the inequality sign.
h>15h > 15
Dividing both sides of an inequality by a negative number reverses the direction of the inequality sign.
4
Determine the smallest integer value for h that satisfies the inequality.
16
Since the time must be strictly greater than 15 hours, the smallest whole number of hours that satisfies this is 16.

Anahtar Kavram

Solving linear inequalities by isolating the variable and reversing the inequality sign when dividing by a negative number.
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Konular

Solving Linear Inequalities

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