Solve for \( x \) 6.1. \( \begin{array}{ll} \\ 6.2 & 6(x-1)=x+4 \\ 6.3 & \frac{x+4}{2}=\frac{2 x+7}{3} \\ 6.4 & \frac{3 x-1}{2}-\frac{2 x}{3}=2\end{array} \)

To solve for \( x \): 6.2: Start with the equation \( 6(x - 1) = x + 4 \). Distributing the \( 6 \) gives \( 6x - 6 = x + 4 \). Subtract \( x \) from both sides to get \( 5x - 6 = 4 \). Then, add \( 6 \) to both sides: \( 5x = 10 \). Finally, divide by \( 5 \): \( x = 2 \). 6.3: For \( \frac{x + 4}{2} = \frac{2x + 7}{3} \), cross-multiply to obtain \( 3(x + 4) = 2(2x + 7) \). This simplifies to \( 3x + 12 = 4x + 14 \). Rearranging gives \( x = -2 \). 6.4: For the equation \( \frac{3x - 1}{2} - \frac{2x}{3} = 2 \), first find a common denominator, which is \( 6 \): \( \frac{3(3x - 1)}{6} - \frac{4x}{6} = 2 \) simplifies to \( \frac{9x - 3 - 4x}{6} = 2 \). Multiply both sides by \( 6 \) to get \( 9x - 4x - 3 = 12 \). This leads to \( 5x - 3 = 12 \), and finally, \( 5x = 15 \), so \( x = 3 \). The solutions are \( x = 2 \) for 6.2, \( x = -2 \) for 6.3, and \( x = 3 \) for 6.4! Happy solving!