Final answer:
To rearrange the equation -7q + 12r = 3q - 4r to solve for q, combine like terms on either side to get -10q = -16r and then divide both sides by -10 to find q = 1.6r. The provided options did not include this correct solution.
Step-by-step explanation:
The student has provided an equation and asked for it to be rearranged so q is the independent variable. The original equation is -7q + 12r = 3q - 4r. To solve for q, we need to perform algebraic rearrangement.
First, let's move all the terms involving q to one side and all other terms to the opposite side:
-7q - 3q = -4r - 12r
Combine like terms:
-10q = -16r
Now, divide both sides by -10 to isolate q:
q = 16r / 10
Finally, simplify the equation:
q = 1.6r
The student's original options did not include this solution, indicating that they possibly made an error in the transcription of the original equation or the provided answer choices.