We are tasked with solving the equation:

\[
15 - q = 3 + \frac{1}{2}q - 1.5
\]

### Step 1: Simplify both sides of the equation
First, simplify the right-hand side by combining constants:

\[
3 - 1.5 = 1.5
\]

Now the equation becomes:

\[
15 - q = 1.5 + \frac{1}{2}q
\]

### Step 2: Eliminate the fraction
To eliminate the fraction, multiply the entire equation by 2:

\[
2(15 - q) = 2\left(1.5 + \frac{1}{2}q\right)
\]

This simplifies to:

\[
30 - 2q = 3 + q
\]

### Step 3: Move terms involving \(q\) to one side
Subtract \(q\) from both sides:

\[
30 - 2q - q = 3
\]

This simplifies to:

\[
30 - 3q = 3
\]

### Step 4: Isolate the variable \(q\)
Subtract 30 from both sides:

\[
-3q = 3 - 30
\]

\[
-3q = -27
\]

### Step 5: Solve for \(q\)
Divide both sides by -3:

\[
q = \frac{-27}{-3} = 9
\]

Thus, the solution is:

\[
q = 9
\]

Would you like more details on any of these steps or have any questions?

Here are 5 related questions you might find interesting:
1. How do you solve an equation with more complex fractions?
2. What are the general steps for solving linear equations?
3. Can you solve an equation with variables on both sides?
4. How do you eliminate decimals in an equation?
5. How do you check if your solution is correct?

**Tip:** Always check your solution by plugging the value back into the original equation to ensure it's correct.

This detailed solution explains how to solve the linear equation 15 - q = 3 + 1/2q - 1.5. It covers important algebraic concepts like eliminating fractions, simplifying both sides, and isolating variables. Suitable for students in Grades 8-10.

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