Final answer:
To make w the independent variable in the equation 4u + 8w = -3u + 2w, combine like terms and solve for w to obtain the rearranged equation w = -7u/6.
Step-by-step explanation:
To rearrange the given equation 4u + 8w = -3u + 2w in terms of w as the independent variable, we need to isolate w on one side of the equation. We can do this by first combining like terms. We'll move all the terms involving u to one side and all the terms involving w to the other.
First, add 3u to both sides of the equation: 4u + 3u + 8w = 2w, which simplifies to 7u + 8w = 2w. Next, subtract 8w from both sides: 7u = 2w - 8w. Combining the w terms gives us 7u = -6w. Finally, to solve for w, divide both sides by -6: w = -7u/6. This gives us w in terms of u, making u the independent variable.