Let's solve the equation to check if $x = -7$ is correct.

The given equation is:

$2x + 7 = x$

1. Subtract $x$ from both sides of the equation:

$2x - x + 7 = x - x$

This simplifies to:

$x + 7 = 0$

2. Subtract 7 from both sides:

$x = -7$

So, $x = -7$ is indeed correct.

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:

1. How would the solution change if the equation was $3x + 7 = x$?
2. What happens if we replace 7 with another number, say 5, in the equation $2x + 5 = x$?
3. Can you solve $4x + 9 = 2x$?
4. What does the solution represent graphically?
5. How do you solve equations with variables on both sides involving fractions?

Tip: Always double-check your solution by substituting the value of $x$ back into the original equation to verify your answer.