Let's solve the equation step by step:

The given equation is: $3b + 10 = -5 - 2b + 8b$

Step 1: Simplify both sides

On the right side, we have $-5 - 2b + 8b$. Combine like terms for the terms with $b$: $-2b + 8b = 6b$ So, the equation becomes: $3b + 10 = -5 + 6b$

Step 2: Move all terms involving $b$ to one side

Subtract $3b$ from both sides to get the terms with $b$ on one side: $10 = -5 + 6b - 3b$ Simplify: $10 = -5 + 3b$

Step 3: Move constant terms to the other side

Add $5$ to both sides: $10 + 5 = 3b$ $15 = 3b$

Step 4: Solve for $b$

Divide both sides by $3$: $b = \frac{15}{3} = 5$

Final Answer:

$b = 5$

Let me know if you need further clarification or have additional questions!

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Here are five related questions you could explore:

1. What are the steps to solve a linear equation with variables on both sides?
2. How do you solve equations with fractions?
3. Can you explain the distributive property and how it applies to solving equations?
4. How do you solve equations with absolute value expressions?
5. What happens when an equation has no solution or infinitely many solutions?

Tip: Always simplify both sides of the equation as much as possible before isolating the variable!