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

Solve for Z. 2/3(Y-Z)=X Z=
Transcript text: Solve for $Z$. \[ \begin{array}{l} \frac{2}{3}(Y-Z)=X \\ Z=\square \end{array} \]
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Solution

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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 \( Z \).

Step 1: Distribute the Coefficient

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

Step 2: Isolate the Term with \(Z\)

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

Step 3: Solve for \(Z\)

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

Final Answer

\[ \boxed{Z = -\frac{3}{2}X + Y} \]

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