https://file.aiquickdraw.com/mathbot/file/1725483981519k9ommtiq.jpg

Let's solve the given equation step by step. The equation in the image is:

\[
3(q + 1) + 1 = 10
\]

### Step 1: Distribute the 3
Distribute the 3 to both terms inside the parentheses:

\[
3 \cdot q + 3 \cdot 1 + 1 = 10
\]

This simplifies to:

\[
3q + 3 + 1 = 10
\]

### Step 2: Combine like terms
Now, combine the constants on the left-hand side:

\[
3q + 4 = 10
\]

### Step 3: Isolate \( q \)
Subtract 4 from both sides:

\[
3q = 10 - 4
\]

\[
3q = 6
\]

### Step 4: Solve for \( q \)
Finally, divide both sides by 3 to isolate \( q \):

\[
q = \frac{6}{3}
\]

\[
q = 2
\]

So, the solution is:

\[
q = 2
\]

Would you like further details or have any questions?

Here are five related questions to explore:

1. How do you handle multi-step equations with variables on both sides?
2. How can you check your solution to ensure it's correct?
3. What happens when you have negative numbers in the equation?
4. How do you solve equations involving fractions?
5. How do you apply the distributive property when solving equations?

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

Learn how to solve the linear equation 3(q + 1) + 1 = 10 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the distributive property and combining like terms, suitable for students in Grades 6-8.

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