1) \( \frac{1}{2} x-\left(\frac{7}{10} x-14\right)-\frac{5}{2}=\frac{3-2 x}{5} \)

To solve the equation \( \frac{1}{2} x-\left(\frac{7}{10} x-14\right)-\frac{5}{2}=\frac{3-2 x}{5} \), we first simplify the left-hand side: 1. Distribute the negative sign: \[ \frac{1}{2} x - \frac{7}{10} x + 14 - \frac{5}{2} = \frac{3 - 2x}{5} \] 2. To combine the terms, we'll convert \( \frac{1}{2} x \) and \( \frac{7}{10} x \) to a common denominator (which is 10): \[ \frac{1}{2} x = \frac{5}{10} x \] 3. Rewriting the left-hand side: \[ \left(\frac{5}{10} x - \frac{7}{10} x\right) + (14 - \frac{5}{2}) = \frac{3 - 2x}{5} \] 4. Combine the x terms: \[ -\frac{2}{10} x + (14 - \frac{5}{2}) = \frac{3 - 2x}{5} \] \[ -\frac{1}{5} x + (14 - 2.5) = \frac{3 - 2x}{5} \] 5. Simplifying \( 14 - \frac{5}{2} \): \[ 14 - 2.5 = 11.5 \] or, \[ 14 - \frac{5}{2} = \frac{28}{2} - \frac{5}{2} = \frac{23}{2} \] 6. Now, plug these values back into the equation: \[ -\frac{1}{5} x + \frac{23}{2} = \frac{3 - 2x}{5} \] 7. To eliminate the fractions, multiply the entire equation by 10: \[ 10\left(-\frac{1}{5} x\right) + 10\left(\frac{23}{2}\right) = 10\left(\frac{3 - 2x}{5}\right) \] \[ -2x + 115 = 6 - 4x \] 8. Now, isolate the variable: \[ -2x + 4x = 6 - 115 \] \[ 2x = -109 \] \[ x = -\frac{109}{2} \] So, the solution to the equation is \( x = -\frac{109}{2} \) or \( -54.5 \).