Let's solve the equation step by step.

The equation is:

\[
4x + 2 = 2x + 22
\]

### Step 1: Move all the terms involving \(x\) to one side of the equation.
Subtract \(2x\) from both sides:

\[
(4x - 2x) + 2 = 22
\]

This simplifies to:

\[
2x + 2 = 22
\]

### Step 2: Move the constant term to the other side.
Subtract 2 from both sides:

\[
2x = 22 - 2
\]

This simplifies to:

\[
2x = 20
\]

### Step 3: Solve for \(x\).
Divide both sides by 2:

\[
x = \frac{20}{2} = 10
\]

So, the solution is:

\[
x = 10
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve linear equations with variables on both sides?
2. What happens if the solution to an equation is not a whole number?
3. Can linear equations have no solution or infinitely many solutions?
4. How can you check if your solution to a linear equation is correct?
5. How do you solve equations with fractions or decimals?

**Tip:** Always verify your solution by substituting it back into the original equation!

Learn how to solve the linear equation 4x + 2 = 2x + 22 with a step-by-step solution. This problem demonstrates essential algebraic techniques such as isolating the variable and simplifying equations. Ideal for students in Grades 6-8.

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