To find the x-intercept of the equation \(2x - 3y = 6\), we set \(y = 0\) and solve for \(x\):
\[ 2x - 3(0) = 6 \implies 2x = 6 \implies x = 3. \]
Thus, the x-intercept of the given equation is \( (3, 0) \).
Next, we need to check which of the provided equations has the same x-intercept, which is \(x = 3\).
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For the equation \(2x - 3y = 8\):
Setting \(y = 0\): \[ 2x - 3(0) = 8 \implies 2x = 8 \implies x = 4. \] (Different x-intercept)
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For the equation \(3x = 3y - 9\):
Rearranging gives \(3x + 9 = 3y\) or \(y = x + 3\).
Setting \(y = 0\): \[ 0 = x + 3 \implies x = -3. \] (Different x-intercept)
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For the equation \(4x = 12 - 5y\):
Rearranging gives \(5y = 12 - 4x\) or \(y = \frac{12 - 4x}{5}\).
Setting \(y = 0\): \[ 0 = 12 - 4x \implies 4x = 12 \implies x = 3. \] (Same x-intercept)
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For the equation \(5x - 5y = 10\):
Rearranging gives \(5y = 5x - 10\) or \(y = x - 2\).
Setting \(y = 0\): \[ 0 = x - 2 \implies x = 2. \] (Different x-intercept)
Among the equations evaluated, the one that has the same x-intercept as the equation \(2x - 3y = 6\) is:
\[ \boxed{4x = 12 - 5y}. \]