Question

1. $x = \frac{2y - z}{4}$

Explanation:

Assuming we need to solve for \( y \) (since the problem isn't specified, we'll do that as a common manipulation).

Step 1: Multiply both sides by 4

To eliminate the denominator, multiply each side of the equation \( x=\frac{2y - z}{4} \) by 4.
\( 4\times x=4\times\frac{2y - z}{4} \)
Simplifying gives \( 4x = 2y - z \).

Step 2: Add \( z \) to both sides

We want to isolate the term with \( y \), so add \( z \) to both sides of \( 4x = 2y - z \).
\( 4x+z = 2y - z+z \)
Simplifying gives \( 4x + z = 2y \).

Step 3: Divide both sides by 2

To solve for \( y \), divide both sides of \( 4x + z = 2y \) by 2.
\( \frac{4x + z}{2}=\frac{2y}{2} \)
Simplifying gives \( y=\frac{4x + z}{2}=2x+\frac{z}{2} \).

Answer:

If solving for \( y \), the solution is \( y = 2x+\frac{z}{2} \) (or \( y=\frac{4x + z}{2} \)).