To solve the equation \( b - 2 + 8b = 35 \), let's first combine like terms.
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Combine \( b \) and \( 8b \): \[ 1b + 8b = 9b \] So the equation becomes: \[ 9b - 2 = 35 \]
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Next, add 2 to both sides to isolate the term with \( b \): \[ 9b - 2 + 2 = 35 + 2 \] Which simplifies to: \[ 9b = 37 \]
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Now, divide both sides by 9 to solve for \( b \): \[ b = \frac{37}{9} \]
Now, we can check our solution by substituting \( b \) back into the original equation:
Substituting \( b = \frac{37}{9} \): \[ b - 2 + 8b = 35 \]
Calculating \( b - 2 \): \[ \frac{37}{9} - 2 = \frac{37}{9} - \frac{18}{9} = \frac{19}{9} \]
Calculating \( 8b \): \[ 8b = 8 \cdot \frac{37}{9} = \frac{296}{9} \]
Adding these results together: \[ \frac{19}{9} + \frac{296}{9} = \frac{19 + 296}{9} = \frac{315}{9} = 35 \]
Since both sides of the equation are equal, the solution is verified.
Thus, the solution is: \[ b = \frac{37}{9} \]