Final answer:
To solve the equation (4/3)w - (1/3) = -(1/4)w - 6 for w, combine like terms and isolate w on one side of the equation. Find the value of w by multiplying both sides of the equation by the reciprocal of the coefficient of w. The simplified answer is w = -38/19.
Step-by-step explanation:
To solve the equation (4/3)w - (1/3) = -(1/4)w - 6, we can start by gathering like terms on one side of the equation. Adding (1/4)w to both sides gives us (4/3)w + (1/4)w - (1/3) = -6. Combining like terms on the left side gives us (19/12)w - (1/3) = -6.
Next, we can isolate w by subtracting (1/3) from both sides: (19/12)w - (1/3) - (1/3) = -6 - (1/3). Simplifying the left side gives us (19/12)w - (2/3) = -6 - (1/3).
Finally, we can multiply both sides of the equation by the reciprocal of (19/12), which is (12/19), to solve for w. The equation becomes w = [(12/19)(-6 - (1/3))] + (2/3). Simplifying the right side gives us the final answer for w.
w = -rac{38}{19}