Let's solve the equation step by step to determine the value of \( x \):
The given equation is: \[ 5(2x + 2) - 7x = 3x + 6. \]
First, distribute the \( 5 \) on the left side: \[ 10x + 10 - 7x = 3x + 6. \]
Now, combine like terms on the left: \[ (10x - 7x) + 10 = 3x + 6, \] which simplifies to: \[ 3x + 10 = 3x + 6. \]
Next, subtract \( 3x \) from both sides: \[ 10 = 6. \]
The statement \( 10 = 6 \) is not true, indicating that there is no value of \( x \) that can satisfy the equation.
Therefore, the conclusion is that the equation has no solution.