Use the addition and division properties of equality to rearrange the equation Q=RS − T

Question

for the quantity of interest S.(3 points)
Responses

S=Q−TR
cap s is equal to the fraction with numerator cap q minus cap t and denominator cap r

S=QRT
cap s is equal to cap q over cap r cap t

S=Q+TR
cap s is equal to the fraction with numerator cap q plus cap t and denominator cap r

S=Q+T−R

Answer 1

To rearrange the equation \( Q = RS - T \) for the quantity of interest \( S \), we can follow these steps using the addition and division properties of equality:

1. Add \( T \) to both sides of the equation: \[ Q + T = RS \]

2. Divide both sides by \( R \): \[ S = \frac{Q + T}{R} \]

So the correct rearranged equation for \( S \) is: \[ S = \frac{Q + T}{R} \]

However, none of the provided responses exactly match this rearrangement. The closest options provided do not accurately reflect the correct manipulation of the original equation.

Here's the breakdown of the options:

1. S=Q−TR: Incorrect.
2. S=QRT: Incorrect.
3. S=Q+TR: Incorrect.
4. S=Q+T−R: Incorrect.

The correct rearrangement should be \( S = \frac{Q + T}{R} \).