Regarding real-life applications, when would a linear inequality be more appropriate to use than a linear equation? Give examples to help me better thanks a lot!

When driving a car, the speed at any time should be less than or equal to the speed limit.

A check written on an account shall not exceed the account balance.

Farrah Farrah answered

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Explain Bot Explain Bot answered

Linear inequalities are used in situations where we need to compare two quantities or determine a range of acceptable values, rather than finding an exact solution. Here are a couple of real-life examples where linear inequalities are more appropriate than linear equations:

1. Speed Limit: When driving a car, the speed at any time should be less than or equal to the speed limit. Suppose the speed limit is 60 miles per hour. You can represent this situation using a linear inequality: "s ≤ 60," where 's' represents the speed of the car. Here, the inequality indicates that the speed should not exceed (be less than) 60 mph. If you were to use a linear equation, you would only find the exact speed value, which is not suitable in this case.

2. Account Balance: A check written on an account should not exceed the account balance. Let's say the account balance is $500. You can express this using a linear inequality as "c ≤ 500," where 'c' represents the check amount. This inequality signifies that the check amount should be less than or equal to $500. If you were to solve this using a linear equation, you would find the exact check amount, rather than ensuring it falls within the permitted range.

In both examples, linear inequalities provide a suitable representation because they allow for a range of acceptable values rather than seeking a single precise solution.