To solve the equation \(-7t - 8 = 10 + 2t\), we will start by isolating \(t\).
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First, let's get all terms involving \(t\) on one side, and constant terms on the other side. We can do this by adding \(7t\) to both sides:
\[ -7t + 7t - 8 = 10 + 2t + 7t \] which simplifies to: \[ -8 = 10 + 9t \]
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Next, we will isolate the \(t\) term by subtracting 10 from both sides:
\[ -8 - 10 = 10 - 10 + 9t \] which simplifies to: \[ -18 = 9t \]
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Now, divide both sides by 9 to solve for \(t\):
\[ t = \frac{-18}{9} \] which simplifies to: \[ t = -2 \]
Thus, the solution is: \[ t = -2 \]
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