To solve the equation \( 4x + 14 = 2x \), follow these steps:

### Step 1: Subtract \( 2x \) from both sides.
\[
4x + 14 - 2x = 2x - 2x
\]
This simplifies to:
\[
2x + 14 = 0
\]

### Step 2: Subtract 14 from both sides.
\[
2x + 14 - 14 = 0 - 14
\]
This simplifies to:
\[
2x = -14
\]

### Step 3: Divide both sides by 2.
\[
\frac{2x}{2} = \frac{-14}{2}
\]
This simplifies to:
\[
x = -7
\]

Thus, the solution is \( x = -7 \).

Would you like more details or have any questions?

Here are some related questions:
1. What is the general process for solving linear equations?
2. How do you solve an equation with variables on both sides?
3. Can you explain the properties of equality used in solving equations?
4. What happens if the solution results in no solution or infinite solutions?
5. How can you check if your solution is correct?

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

Learn how to solve the linear equation 4x + 14 = 2x with a clear, step-by-step breakdown. This solution covers essential algebraic concepts, such as subtracting variables and dividing to isolate the unknown. Suitable for students in Grades 6-8.

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