Question

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Part 1
Solve the equation. Check your answer.
bminus2plus8bequals35

Answer 1

To solve the equation \( b - 2 + 8b = 35 \), let's first combine like terms.

1. Combine \( b \) and \( 8b \):
\[
1b + 8b = 9b
\]
So the equation becomes:
\[
9b - 2 = 35
\]

2. Next, add 2 to both sides to isolate the term with \( b \):
\[
9b - 2 + 2 = 35 + 2
\]
Which simplifies to:
\[
9b = 37
\]

3. 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:
\[
b = \frac{37}{9}
\]