\( \frac { x , 5 } { 2 } + \frac { 4 x - 5 } { 3 } - \frac { 1 } { 6 } = \frac { 7 } { 12 } x + \frac { 5 } { 6 } \)

To solve the equation \( \frac { x , 5 } { 2 } + \frac { 4 x - 5 } { 3 } - \frac { 1 } { 6 } = \frac { 7 } { 12 } x + \frac { 5 } { 6 } \), first clarify the fraction \( \frac{x, 5}{2} \), since it’s not standard notation. If you meant \( \frac{5}{2}x \) instead, you can proceed by rewriting the equation: 1. Rewrite the equation properly: \[ \frac{5}{2}x + \frac{4x - 5}{3} - \frac{1}{6} = \frac{7}{12}x + \frac{5}{6} \] 2. Find a common denominator, which in this case would be 12. Rewrite each term: \[ \frac{30}{12}x + \frac{16x - 20}{12} - \frac{2}{12} = \frac{7}{12}x + \frac{10}{12} \] 3. Combine the left side: \[ \frac{30x + 16x - 20 - 2}{12} = \frac{7}{12}x + \frac{10}{12} \] This simplifies to: \[ \frac{46x - 22}{12} = \frac{7}{12}x + \frac{10}{12} \] 4. Clear the denominators by multiplying through by 12: \[ 46x - 22 = 7x + 10 \] 5. Rearranging gives: \[ 46x - 7x = 10 + 22 \] \[ 39x = 32 \] \[ x = \frac{32}{39} \] So, the solution to the equation is \( x = \frac{32}{39} \).