To solve the equation $2x + 4x + 2 = x + x + 10$, let's go through it step-by-step:

Step 1: Simplify both sides of the equation

1. Combine like terms on each side.
   • Left side: $2x + 4x + 2 = 6x + 2$
   • Right side: $x + x + 10 = 2x + 10$

So, the equation now becomes: $6x + 2 = 2x + 10$

Step 2: Isolate the variable

2. Subtract $2x$ from both sides to bring all $x$-terms to one side: $6x - 2x + 2 = 10$ This simplifies to: $4x + 2 = 10$

3. Subtract 2 from both sides to isolate terms with $x$: $4x = 8$

4. Divide both sides by 4 to solve for $x$: $x = 2$

Solution

The solution to the equation is: $x = 2$

Would you like further details or have any questions about this solution?

Here are some related questions to explore:

1. How can you verify the solution to this equation?
2. What happens if you substitute a different value for $x$ in the original equation?
3. How do equations change when we add or subtract the same term from both sides?
4. What is the effect of dividing both sides by a non-zero constant in an equation?
5. Can you solve a similar equation with different coefficients?

Tip: Always check your solution by substituting it back into the original equation to ensure both sides are equal.