https://file.aiquickdraw.com/mathbot/file/1725577346292pgs0yema.jpg

The equation provided is:

\[
T = \frac{1}{7}(x - y + z)
\]

We are tasked with solving for \(z\). Let's go step by step.

### Step 1: Eliminate the fraction.
Multiply both sides of the equation by 7 to remove the fraction:

\[
7T = x - y + z
\]

### Step 2: Solve for \(z\).
Now, isolate \(z\) by subtracting \((x - y)\) from both sides:

\[
z = 7T - (x - y)
\]

Simplifying the right-hand side:

\[
z = 7T - x + y
\]

Thus, the solution for \(z\) is:

\[
z = 7T - x + y
\]

Would you like a more detailed explanation, or do you have any further questions?

Here are five related questions you can explore:

1. What happens if \(T = 0\) in the equation? 
2. How would you solve for \(x\) instead of \(z\)?
3. Can you plot the equation \(z = 7T - x + y\) for specific values of \(T\), \(x\), and \(y\)?
4. How does the equation change if the coefficient \(\frac{1}{7}\) was something else?
5. What if \(y = 0\), how does the equation simplify for \(z\)?

**Tip:** Always clear fractions early in equations to simplify solving.

Solve the following equation for z: T = 1/7(x - y + z)

Learn how to solve the equation T = 1/7(x - y + z) for z with a clear step-by-step breakdown. This problem covers key algebraic concepts, such as eliminating fractions and isolating variables. Suitable for students in Grades 8-10.

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