To solve the equation \( 4x = 3(x + 5) - 15 \), we start by simplifying both sides.
First, simplify the right side:
\[ 3(x + 5) = 3x + 15 \] Now substitute back into the equation:
\[ 4x = 3x + 15 - 15 \]
This simplifies to:
\[ 4x = 3x \]
Next, subtract \( 3x \) from both sides:
\[ 4x - 3x = 0 \] \[ x = 0 \]
Now let's analyze the result. We found that \( x = 0 \) is a solution.
To also determine the type of solution, consider the steps we took:
If the equation simplifies to a true statement with no variable remaining (like \( 0 = 0 \)), then there would be infinite solutions. If it simplifies to a contradiction (like \( 0 = 5 \)), there would be no solution. In our case, we ended up with one variable solution.
Thus, the final conclusion is:
The equation has one solution: \( x = 0 \).