To model the equation \(-x + 40 = x\) with a real-world problem, we need to interpret the components of the equation.
- Variables:
- Let \(x\) represent the amount gained (or achieved in any context).
- The term \(-x\) would then represent the amount lost (or negative change).
- The constant \(40\) specifies a fixed amount that makes a comparison.
Now, let's analyze each of the provided options:
-
The amount of money a stock lost in the stock market was $40 more than it gained.
- This can be written as \(-x = x + 40\), which simplifies to the same equation. (This does not exactly match, as it should represent losing an amount that is equal to the amount gained plus $40.)
-
Marsha is below sea level. To get as far above sea level as she is below, she would have to move to a location 40 feet higher.
- This can be interpreted as Marsha being \(x\) feet below sea level, thus needing to overcome her depth \(x\) and also adds another 40 feet to be above sea level. This does work out to represent a similar equation but is still a bit nuanced.
-
If Alex gained as much money as she lost, she would have 40 dollars.
- Here, this can be interpreted as saying Alex lost \(x\) dollars and gained \(x + 40\) dollars. This does not match our equation.
-
The number of days that the temperature has been below zero is 40 fewer than the number of days the temperature has been above zero.
- Here, if we say \(x\) represents the number of days above zero, then \(-x + 40 = x\) perfectly models the situation, since it indicates that the count of days below is \(40\) less than those above.
The closest option that accurately models the equation \(-x + 40 = x\) is:
The number of days that the temperature has been below zero is 40 fewer than the number of days the temperature has been above zero.