To determine the number of solutions for the equation \(7x - 6 + 3 = 5x + 2x + 5\), let's simplify both sides step by step.
Starting with the left side:
\[ 7x - 6 + 3 = 7x - 3 \]
Now, simplifying the right side:
\[ 5x + 2x + 5 = 7x + 5 \]
Now the equation is:
\[ 7x - 3 = 7x + 5 \]
Next, we will subtract \(7x\) from both sides:
\[ -3 = 5 \]
This is a false statement, which means there is no value of \(x\) that can satisfy the equation.
Since the equation leads to a contradiction, the best description of the number of solutions is:
D: no solution.
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