Final answer:
After simplifying the given equation by combining like terms and isolating the variable w, the solution is found to be w = 11, which is not listed in the provided options.
Step-by-step explanation:
To solve the equation (3/7)w - 11 = -(4/7)w, we must first combine like terms. To do this, we add (4/7)w to both sides of the equation:
(3/7)w + (4/7)w - 11 = 0
Now we have a common denominator, so we combine the w terms:
(3/7 + 4/7)w - 11 = 0
(7/7)w - 11 = 0
Since 7/7 is equal to 1, we have:
w - 11 = 0
Now, we add 11 to both sides of the equation to solve for w:
w = 11
Thus, none of the provided options (a) w = 7, (b) w = -7, (c) w = 4, (d) w = -4 is correct. The correct answer is w = 11.