Question - Solving a Linear Equation with Variables on Both Sides

Begin by expanding the terms within the parentheses:

\[2(3x + 5) - 3(3x - 1) = 3(4 - x)\]

\[6x + 10 - 9x + 3 = 12 - 3x\]

Combine like terms:

\[-3x + 13 = 12 - 3x\]

Add \(3x\) to both sides to move variables to one side:

\[-3x + 3x + 13 = 12 - 3x + 3x\]

\[13 = 12\]

Since 13 is not equal to 12, we have an inconsistency. The equation has no solution because it is not an identity, and the two sides of the equation are not equal for any value of \(x\).