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

**6.2 Solve for \( x \) in the equation \( 6(x-1)=x+4 \):** 1. Expand the left-hand side: \[ 6x - 6 = x + 4 \] 2. Subtract \( x \) from both sides: \[ 6x - x - 6 = 4 \quad \Rightarrow \quad 5x - 6 = 4 \] 3. Add 6 to both sides: \[ 5x = 10 \] 4. Divide by 5: \[ x = 2 \] --- **6.3 Solve for \( x \) in the equation \(\frac{x+4}{2}=\frac{2x+7}{3}\):** 1. Cross-multiply to eliminate the fractions: \[ 3(x+4)=2(2x+7) \] 2. Expand both sides: \[ 3x + 12 = 4x + 14 \] 3. Subtract \( 3x \) from both sides: \[ 12 = x + 14 \] 4. Subtract 14 from both sides: \[ x = -2 \] --- **6.4 Solve for \( x \) in the equation \(\frac{3x-1}{2}-\frac{2x}{3}=2\):** 1. Find a common denominator for the fractions, which is 6, and rewrite the equation: \[ \frac{3(3x-1) - 4x}{6} = 2 \] 2. Expand the numerator: \[ \frac{9x - 3 - 4x}{6} = \frac{5x - 3}{6} = 2 \] 3. Multiply both sides by 6 to eliminate the denominator: \[ 5x - 3 = 12 \] 4. Add 3 to both sides: \[ 5x = 15 \] 5. Divide by 5: \[ x = 3 \]