To solve the equation \( 5.5(2m - 1) + 0.5m = 8.5m - 1 \), we first distribute \( 5.5 \) on the left side:
\[ 5.5 \times 2m - 5.5 \times 1 + 0.5m = 8.5m - 1 \] \[ 11m - 5.5 + 0.5m = 8.5m - 1 \]
Next, we combine the \( m \) terms on the left side:
\[ 11m + 0.5m - 5.5 = 8.5m - 1 \] \[ 11.5m - 5.5 = 8.5m - 1 \]
Now we need to isolate the \( m \) terms. We can subtract \( 8.5m \) from both sides:
\[ 11.5m - 8.5m - 5.5 = -1 \] \[ 3m - 5.5 = -1 \]
Next, add \( 5.5 \) to both sides:
\[ 3m = -1 + 5.5 \] \[ 3m = 4.5 \]
Now, divide by \( 3 \):
\[ m = \frac{4.5}{3} = 1.5 \]
So, the value of \( m \) is
\[ \boxed{1.5} \]
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