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The given equation is:

\[
9 + 4q = 13 + 3q
\]

### Step 1: Isolate the variable \(q\).
Subtract \(3q\) from both sides:

\[
9 + 4q - 3q = 13 + 3q - 3q
\]

Simplifying:

\[
9 + q = 13
\]

### Step 2: Solve for \(q\).
Subtract 9 from both sides:

\[
q = 13 - 9
\]

\[
q = 4
\]

### Step 3: Check the solution.
Substitute \(q = 4\) back into the original equation:

\[
9 + 4(4) = 13 + 3(4)
\]

\[
9 + 16 = 13 + 12
\]

\[
25 = 25
\]

Since both sides are equal, the solution \(q = 4\) is correct.

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Here are 5 related questions for further practice:
1. Solve \(7 + 5x = 12 + 4x\).
2. Solve \(6 + 3y = 2 + 2y\).
3. Solve \(10 + 2n = 8 + n\).
4. Solve \(5p + 7 = 2p + 13\).
5. Solve \(3 + 6r = 5 + 5r\).

**Tip**: Always double-check your solution by substituting it back into the original equation.

Learn how to solve the linear equation 9 + 4q = 13 + 3q with a clear step-by-step solution. This problem demonstrates isolating variables and applying basic algebraic techniques, perfect for students in Grades 6-8.

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