Let's solve the equation step by step to determine how many solutions it has:
The equation given is: \[ 4(x + 5) - 5 = \frac{8x + 18}{2} \]
First, simplify the left side: \[ 4(x + 5) - 5 = 4x + 20 - 5 = 4x + 15 \]
Now simplify the right side: \[ \frac{8x + 18}{2} = 4x + 9 \]
Now we can rewrite the equation as: \[ 4x + 15 = 4x + 9 \]
Next, let's subtract \( 4x \) from both sides: \[ 15 = 9 \]
This statement, \( 15 = 9 \), is false. Therefore, there are no values of \( x \) that can satisfy this equation.
The correct answer is: A) no solutions.
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