Let's go through the given equation step by step to determine the number of solutions.
The equation you provided is: \[ 6x + 3 = 5(x + 3) \]
First, let's expand the right side: \[ 6x + 3 = 5x + 15 \]
Next, let's move all terms involving \( x \) to one side and constant terms to the other side: \[ 6x - 5x = 15 - 3 \] \[ x = 12 \]
We found a solution \( x = 12 \).
Now, let's assess how many solutions this equation has. Since we were able to isolate \( x \) and arrived at a single value, it indicates that the equation has exactly one unique solution.
To confirm, we can also check if substituting \( x = 12 \) back into the very original equation holds true: \[ 6(12) + 3 = 5(12 + 3) \] \[ 72 + 3 = 5(15) \] \[ 75 = 75 \]
Since both sides of the equation are equal, \( x = 12 \) is indeed a solution.
Therefore, the equation \( 6x + 3 = 5(x + 3) \) has one solution: \( x = 12 \).
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