To isolate \( S \) in the equation \( Q = RS - T \), we can follow these steps using the addition and division properties of equality:
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First, add \( T \) to both sides of the equation to eliminate \( -T \) from the right side: \[ Q + T = RS \]
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Next, divide both sides by \( R \) to solve for \( S \): \[ S = \frac{Q + T}{R} \]
Since none of the provided options directly lists \( S = \frac{Q + T}{R} \), let's analyze the options, ensuring we adhere closely to what we derived.
We should note that if we separate the terms in the numerator, we could also express this as: \[ S = \frac{Q}{R} + \frac{T}{R} \]
However, since the options are limited and none directly match the rearrangement we derived, we have to check if the expression can be transformed into something among the suggestions.
To verify against provided choices:
- A: \( S = \frac{Q}{RT} \) (Incorrect: the expression doesn't match)
- B: \( S = \frac{Q + T}{R} \) can be rewritten from our work, but it's not among your given choices.
- C: \( S = \frac{Q - T}{R} \) (Incorrect: this would have resulted from a subtraction)
- D: \( S = Q + T - R \) (Incorrect: it's not the equivalent expression)
Given the choices, we conclude that additional manipulation isn’t yielding any match, so the answer is primarily \( S = \frac{Q + T}{R} \), but none of the listed options effectively represent the isolated \( S \) correctly.
If a different interpretation is required, you might need to double-check for potential typos or errors in the options provided.
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