To solve the equation \(1 + 5x = 2x + 16\), follow these steps:

### Step 1: Move the terms involving \(x\) to one side.
Subtract \(2x\) from both sides:
\[
1 + 5x - 2x = 16
\]
Simplifying:
\[
1 + 3x = 16
\]

### Step 2: Move the constant terms to the other side.
Subtract \(1\) from both sides:
\[
3x = 16 - 1
\]
Simplifying:
\[
3x = 15
\]

### Step 3: Solve for \(x\).
Divide both sides by \(3\):
\[
x = \frac{15}{3}
\]
Simplifying:
\[
x = 5
\]

Thus, the solution is \(x = 5\).

Would you like a detailed explanation of any of the steps or have any questions?

### Related Questions:
1. How do you solve an equation with fractions?
2. What happens if an equation has no solution?
3. Can you explain how to solve a quadratic equation?
4. How do you handle equations with variables on both sides?
5. What is the difference between an equation and an inequality?

### Tip: 
Always simplify both sides of the equation as much as possible before moving terms.

Learn how to solve the linear equation 1 + 5x = 2x + 16 with a detailed step-by-step solution. This problem covers essential algebraic concepts, including solving linear equations with variables on both sides and using the transposition method. Suitable for students in Grades 6-8.

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