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.<br /><br />First, expand both sides of the equation:<br />\[ 2(3x + 5) = 2(2x - 3) + 2x \]<br /><br />This simplifies to:<br />\[ 6x + 10 = 4x - 6 + 2x \]<br /><br />Combine like terms on the right side:<br />\[ 6x + 10 = 6x - 6 \]<br /><br />Next, subtract \(6x\) from both sides to isolate the constants:<br />\[ 10 = -6 \]<br /><br />This statement is clearly false, indicating that there is no value of \(x\) that satisfies the equation. Therefore, the equation has no solutions.<br /><br />So, the correct answer is:<br />There are no solutions.