The given equation is:

\[
x \cdot 1 + 2 \cdot x \cdot 1 = 52
\]

Simplify it:

\[
x + 2x = 52
\]

Combine like terms:

\[
3x = 52
\]

Now, solve for \(x\) by dividing both sides by 3:

\[
x = \frac{52}{3} = 17.33
\]

So, the solution is:

\[
x = 17.33
\]

Would you like further details or have any questions?

Here are some related questions for practice:
1. Solve \(4x + 5x = 72\).
2. Solve \(3x + 7 = 58\).
3. If \(2x + 3 = 45\), find \(x\).
4. What is the value of \(x\) if \(x - 3x + 9 = 15\)?
5. Solve the equation \(5x + 2 = 3x + 18\).

**Tip**: Always combine like terms before solving for the variable to simplify the equation quickly.

Learn how to solve the linear equation x + 2x = 52 with a detailed step-by-step solution. This problem covers key algebraic concepts, including combining like terms and solving for variables. Suitable for students in Grades 6-8.

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