In your journal, you made up an inequality and solved it. You also brainstormed what it would look like to communicate your solution clearly if your inequality represented a real-world problem. In your first post, share your inequality and solution with your peers. Then ask your peers if they can come up with a real-world problem that could be solved using your inequality.
Next, read your peers’ inequalities. Respond to two of your peers by providing a unique real-world problem that could be solved with their inequality. Explain what if would look like to communicate the solution to your real-world problem clearly.
Peer 1:
Inequality: 2x + 5 > 13
Solution:
To solve the inequality, we subtract 5 from both sides:
2x > 13 - 5
2x > 8
And then divide both sides by 2:
x > 8/2
x > 4
Therefore, the solution to the inequality is x > 4.
Real-world problem:
This inequality can be used to solve a real-world problem related to buying movie tickets. Let's say the cost of a movie ticket is $5 and we have $13 in our pocket. We would like to know how many movie tickets we can buy with the money we have. The inequality 2x + 5 > 13 can help us determine the maximum number of tickets we can purchase.
To communicate the solution clearly, we would explain that in order to find the maximum number of tickets, we need to solve the inequality. By subtracting 5 from both sides and dividing both sides by 2, we find that x > 4. This means that we can buy a maximum of 4 movie tickets with $13. We would clearly communicate that the inequality represents the limit on the number of tickets we can afford with the given amount of money.
Peer 2:
Inequality: 3y - 7 ≤ 14
Solution:
To solve the inequality, we add 7 to both sides:
3y ≤ 14 + 7
3y ≤ 21
And then divide both sides by 3:
y ≤ 21/3
y ≤ 7
Therefore, the solution to the inequality is y ≤ 7.
Unique real-world problem:
This inequality can be used to solve a real-world problem related to a car's fuel tank capacity. Let's say a car has a fuel tank with a capacity of 14 gallons. We want to determine how many miles the car can travel with the given amount of fuel. The inequality 3y - 7 ≤ 14 can help us find the maximum distance the car can travel in miles.
To communicate the solution clearly, we would explain that by adding 7 to both sides of the inequality and dividing both sides by 3, we find that y ≤ 7. This means that the car can travel a maximum of 7 miles with the fuel capacity of 14 gallons. We would clearly communicate that the inequality represents the limit on the distance the car can travel with the given fuel.