Question

Find Q in the following equation:

Q±Q = A±A + B±B - C±C
A) A+B+C
B) A-B-C
C) A-B+C
D) A+B-C

Answer 1

By simplifying the equation through doubling or nullifying terms, the correct answer is found to be
`Q = A + B - C`, which corresponds to option D.

Step-by-step explanation:

To find Q in the given equation
`Q±Q = A±A + B±B - C±C`, let's simplify the equation by considering the operations. If
`Q` is added or subtracted to itself, the result is either
`2Q or 0`, since anything plus or minus itself is doubled or nullified. Similarly, for
`A, B, and C` the equation
`A±A` simplifies to
`2A or 0 B±B`simplifies to
`2B or 0 and C±C` simplifies to
`2C or 0`. However, since
`0` cannot be combined with other terms to produce any meaningful differences in this context, we should assume the operation is always addition for this exercise.

Therefore,
`2Q = 2A + 2B - 2C` and upon dividing the entire equation by
`2`we are left with
`Q = A + B - C.`

This simplification tells us the correct answer is option D)
`A + B - C`.