Final answer:
To solve for x in the equation 8x = 40 - 32, no algebraic rearrangement is necessary as it stands. If the equation was meant to include a variable 'A', such as in 8x = 40 - 32A, then further information on 'A' is needed to solve for 'x'. If the correct equation was simply 8x = 40, then x = 5 after dividing both sides by 8.
Step-by-step explanation:
To solve for x, we begin by isolating the variable on one side of the equation. In the equation 8x = 40 - 32, we do not have a variable on the right side of the equation, so we can simply add or subtract to get x alone. Following the principles of algebraic manipulation, subtraction of the same number on both sides of an equation maintains the equality. Hence, subtracting 32 from both sides would not be appropriate as there is no 32 to subtract on the left side.
Instead, if the equation to solve was misread and should be 8x = 40 - 32A, where 'A' is a constant, then we subtract '40' from each side to yield 8x - 40 = -32A. Since 'A' is not defined in the question, we stop here and cannot further simplify or solve for 'x' without additional information on 'A'.
If the student meant to ask about the equation 8x = 40, then we would divide both sides of the equation by 8 to isolate x, which would give us x = 5.