Let's solve the equation:

\[
15 = \frac{1}{2} + \frac{3}{2}x + 10
\]

### Step 1: Combine like terms on the right-hand side.
\[
\frac{1}{2} + 10 = \frac{1}{2} + \frac{20}{2} = \frac{21}{2}
\]
So the equation becomes:
\[
15 = \frac{21}{2} + \frac{3}{2}x
\]

### Step 2: Subtract \(\frac{21}{2}\) from both sides.
\[
15 - \frac{21}{2} = \frac{3}{2}x
\]

Convert 15 to a fraction with denominator 2:
\[
15 = \frac{30}{2}
\]
Now subtract:
\[
\frac{30}{2} - \frac{21}{2} = \frac{9}{2}
\]

So:
\[
\frac{9}{2} = \frac{3}{2}x
\]

### Step 3: Solve for \(x\).
To isolate \(x\), multiply both sides by \(\frac{2}{3}\):
\[
x = \frac{9}{2} \times \frac{2}{3} = \frac{18}{6} = 3
\]

Thus, the solution is:
\[
x = 3
\]

Would you like further clarification on any of the steps? Here are 5 related questions to explore:

1. How do you solve linear equations involving fractions?
2. What is the method to simplify complex fractions?
3. How would you graph the equation \(\frac{1}{2} + \frac{3}{2}x + 10 = y\)?
4. What are common strategies to eliminate fractions in algebraic equations?
5. Can this equation be solved using substitution or graphing methods?

**Tip**: Always check your answer by substituting it back into the original equation to ensure it holds true.

Learn how to solve the linear equation 15 = 1/2 + 3/2x + 10. This step-by-step guide simplifies the equation by eliminating fractions and solving for x, a crucial skill for students in Grades 6-8 studying algebra and linear equations.

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