How many solutions does the following equation have? 2(3x+5)=2(2x-3)+2x There are no solutions. There are infinitely many solutions. There are two solutions. There is one solution.

To determine the number of solutions for the equation \(2(3x+5)=2(2x-3)+2x\), we need to simplify and solve it step by step.First, expand both sides of the equation: This simplifies to: Combine like terms on the right side: Next, subtract from both sides to isolate the constants: This statement is clearly false, indicating that there is no value of that satisfies the equation. Therefore, the equation has no solutions.So, the correct answer is:There are no solutions.