Question

Which equation is equivalent to w=x+y−z ?

z=w−x−y

z=x+y−w

z=(x+y)w

z=x+y+w

Answer 1

To determine which equation is equivalent to \( w = x + y - z \), we can rearrange this equation to solve for \( z \).

Starting with the original equation:

\[
w = x + y - z
\]

We can add \( z \) to both sides:

\[
w + z = x + y
\]

Now, subtract \( w \) from both sides to isolate \( z \):

\[
z = x + y - w
\]

This matches one of the provided options. Rearranging it, we can also express it as:

\[
z = x + y - w
\]

To see which option this corresponds to, let's look at the given options:

1. \( z = w - x - y \) (not equivalent)
2. \( z = x + y - w \) (this matches)
3. \( z = (x + y)w \) (not equivalent)
4. \( z = x + y + w \) (not equivalent)

Thus, the equation that is equivalent to \( w = x + y - z \) is:

\[
\boxed{z = x + y - w}
\]