To model the equation \(-x + 40 = x\), we want to create a real-world problem that represents the relationship described by the equation.
The equation essentially states that a certain loss, represented by \(-x\), combined with 40 results in the same value as a certain gain, represented by \(x\).
Let's break down the options provided:
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The amount of money a stock lost in the stock market was $40 more than it gained.
- This statement can be represented as \( -x = x + 40\), which is not the same as our equation.
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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 could represent a balance of her current position below sea level and the additional height needed, but it more closely fits a different model.
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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.
- This can be represented as \( -x = x - 40\). This model does not fit our equation either.
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If Alex gained as much money as she lost, she would have 40 dollars.
- This can be expressed as \( -x + 40 = x\), which correctly models the concept of having $40 additional after losses equal to gains.
Based on the analysis, the best real-world problem that models the equation \(-x + 40 = x\) is:
If Alex gained as much money as she lost, she would have 40 dollars.
1 answer