Questions: Solve for Z. 2/3(Y-Z)=X Z=

Solution Steps

To solve for \( Z \) in the equation \(\frac{2}{3}(Y-Z)=X\), we need to isolate \( Z \) on one side of the equation. Start by distributing the \(\frac{2}{3}\) across the terms inside the parentheses, then rearrange the equation to solve for \( Z \).

Start with the equation: \[ \frac{2}{3}(Y-Z) = X \] Distribute \(\frac{2}{3}\) across the terms inside the parentheses: \[ \frac{2}{3}Y - \frac{2}{3}Z = X \]

Rearrange the equation to isolate the term with \(Z\): \[ -\frac{2}{3}Z = X - \frac{2}{3}Y \]

Multiply both sides by \(-\frac{3}{2}\) to solve for \(Z\): \[ Z = -\frac{3}{2}X + Y \]

Final Answer