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

A. z = (x + y) / w
B. z = x + y + w
C. z = w - x - y
D. z = x + y - w

3 answers

To find an equation equivalent to \( w = x + y - z \), we can manipulate this original equation to isolate \( z \).

Starting with the original equation:

\[ w = x + y - z \]

We can rearrange it to solve for \( z \):

  1. Add \( z \) to both sides: \[ w + z = x + y \]

  2. Next, subtract \( w \) from both sides to isolate \( z \): \[ z = x + y - w \]

Now, let's compare this with the options given:

A. \( z = \frac{x + y}{w} \) — Not equivalent.

B. \( z = x + y + w \) — Not equivalent.

C. \( z = w - x - y \) — Not equivalent.

D. \( z = x + y - w \) — This is equivalent to what we derived.

The correct answer is:

D. \( z = x + y - w \)

are you sure this is correct

Let's go through the steps again to verify the calculations.

Starting with the equation given:

\[ w = x + y - z \]

We want to isolate \( z \). To do this, we can rearrange the equation:

  1. Add \( z \) to both sides and subtract \( w \) from both sides: \[ z = x + y - w \]

Now we have \( z \) expressed in terms of \( w, x, \) and \( y \):

\[ z = x + y - w \]

Now let’s check each option:

A. \( z = \frac{x + y}{w} \) — Not equivalent.

B. \( z = x + y + w \) — Not equivalent.

C. \( z = w - x - y \) — Not equivalent.

D. \( z = x + y - w \) — This is equivalent to what we derived.

So upon review, we confirm that the correct answer is indeed:

D. \( z = x + y - w \)

If you have any further questions or need clarification on a specific part, feel free to ask!