Let's solve the equation:

\[
x + 2 + 3 = 6 + 2x
\]

### Step 1: Simplify both sides
\[
x + 5 = 6 + 2x
\]

### Step 2: Move the \(x\) terms to one side
Subtract \(x\) from both sides:
\[
5 = 6 + x
\]

### Step 3: Isolate \(x\)
Subtract 6 from both sides:
\[
5 - 6 = x
\]
\[
x = -1
\]

Thus, the solution is:
\[
x = -1
\]

Do you need any further explanation or have any questions?

Here are five related questions to expand on this topic:
1. How do you solve equations with variables on both sides?
2. What are common mistakes when solving linear equations?
3. How do you check if your solution to an equation is correct?
4. What happens if there is no solution to an equation?
5. How do you solve an equation with fractions?

**Tip:** Always check your solution by substituting the value of the variable back into the original equation!

Learn how to solve the linear equation x + 2 + 3 = 6 + 2x with a detailed step-by-step solution. This problem demonstrates key algebraic principles, including isolating variables and simplifying both sides. Suitable for students in Grades 6-8.

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