To solve for \(y\) in the equation:

\[
X = \frac{2y - z}{4}
\]

we need to isolate \(y\). Let's follow the steps to do that.

1. **Multiply both sides by 4 to eliminate the denominator:**

\[
4X = 2y - z
\]

2. **Add \(z\) to both sides to isolate the \(2y\) term:**

\[
4X + z = 2y
\]

3. **Divide both sides by 2 to solve for \(y\):**

\[
y = \frac{4X + z}{2}
\]

4. **Simplify the expression:**

\[
y = 2X + \frac{z}{2}
\]

So, the solution for \(y\) in terms of \(X\) and \(z\) is:

\[
\boxed{y = 2X + \frac{z}{2}}
\]

Would you like more details or have any questions?

### Relative Questions:

1. How would the solution change if the equation were \(X = \frac{2y + z}{4}\) instead?
2. What if \(X = \frac{2y - z}{4}\) and you wanted to solve for \(z\) instead?
3. How can you verify that your solution for \(y\) is correct?
4. If \(y = 2X + \frac{z}{2}\), what happens to \(y\) when \(X = 0\) and \(z = 4\)?
5. How would you graph the relationship between \(y\) and \(X\) given \(z = 3\)?

### Tip:

When solving for a variable, remember to perform the same operation on both sides of the equation to maintain the equality.

Learn how to solve the equation (2y - z) / 4 for y with a detailed step-by-step solution. This problem covers key algebraic concepts, including linear equations and variable isolation. Suitable for students in Grades 7-9.

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