To solve the equation \(7x - 6 + 3 = 5x + 2x + 5\), we start by simplifying both sides.
First, simplify the left side: \[ 7x - 6 + 3 = 7x - 3 \]
Now simplify the right side: \[ 5x + 2x + 5 = 7x + 5 \]
Now the equation looks like this: \[ 7x - 3 = 7x + 5 \]
Next, subtract \(7x\) from both sides: \[ -3 = 5 \]
This statement is false, indicating that there is no value of \(x\) that can satisfy the equation. Therefore, there are no solutions to the equation.
The BEST description of the number of solutions for the given equation is:
D. no solution