f) \( 2(7 x-1)-3(4-14 x)=-6 \quad S=\left\{\frac{1}{7}\right\} \) g) \( -61=2(y+7)-3(3-3 y) \quad S=\{-6\} \) h) \( x+3(x-1)-(x+9)=-147 \quad S=\{-45\} \) i) \( t-3(4-t)=-96 \quad S=\{-21\} \) j) \( k-(3-k)=1 \quad S=\{2\} \)

Let's solve each equation step by step. ### f) \( 2(7x - 1) - 3(4 - 14x) = -6 \) 1. Distribute: \[ 14x - 2 - 12 + 42x = -6 \] 2. Combine like terms: \[ 56x - 14 = -6 \] 3. Add 14 to both sides: \[ 56x = 8 \] 4. Divide by 56: \[ x = \frac{8}{56} = \frac{1}{7} \] **Solution:** \( S = \left\{ \frac{1}{7} \right\} \) --- ### g) \( -61 = 2(y + 7) - 3(3 - 3y) \) 1. Distribute: \[ -61 = 2y + 14 - 9 + 9y \] 2. Combine like terms: \[ -61 = 11y + 5 \] 3. Subtract 5 from both sides: \[ -66 = 11y \] 4. Divide by 11: \[ y = -6 \] **Solution:** \( S = \{-6\} \) --- ### h) \( x + 3(x - 1) - (x + 9) = -147 \) 1. Distribute: \[ x + 3x - 3 - x - 9 = -147 \] 2. Combine like terms: \[ 3x - 12 = -147 \] 3. Add 12 to both sides: \[ 3x = -135 \] 4. Divide by 3: \[ x = -45 \] **Solution:** \( S = \{-45\} \) --- ### i) \( t - 3(4 - t) = -96 \) 1. Distribute: \[ t - 12 + 3t = -96 \] 2. Combine like terms: \[ 4t - 12 = -96 \] 3. Add 12 to both sides: \[ 4t = -84 \] 4. Divide by 4: \[ t = -21 \] **Solution:** \( S = \{-21\} \) --- ### j) \( k - (3 - k) = 1 \) 1. Distribute: \[ k - 3 + k = 1 \] 2. Combine like terms: \[ 2k - 3 = 1 \] 3. Add 3 to both sides: \[ 2k = 4 \] 4. Divide by 2: \[ k = 2 \] **Solution:** \( S = \{2\} \) --- In summary, the solutions are: - f) \( S = \left\{ \frac{1}{7} \right\} \) - g) \( S = \{-6\} \) - h) \( S = \{-45\} \) - i) \( S = \{-21\} \) - j) \( S = \{2\} \)