d) \( (3 x-2): 0,15=6: 5 \) e) \( (x+2): \frac{1}{2}=2: 1 \) f) \( (x-1): 4=3: 5 \)

Let's solve each of the given proportions for \( x \). --- ### **d) \( \frac{3x - 2}{0.15} = \frac{6}{5} \)** **Step 1:** Set up the equation from the proportion: \[ \frac{3x - 2}{0.15} = \frac{6}{5} \] **Step 2:** Cross-multiply to eliminate the fractions: \[ (3x - 2) \times 5 = 6 \times 0.15 \] \[ 5(3x - 2) = 0.9 \] **Step 3:** Distribute the 5: \[ 15x - 10 = 0.9 \] **Step 4:** Add 10 to both sides: \[ 15x = 10.9 \] **Step 5:** Divide both sides by 15 to solve for \( x \): \[ x = \frac{10.9}{15} = \frac{109}{150} \approx 0.727 \] --- ### **e) \( \frac{x + 2}{\frac{1}{2}} = \frac{2}{1} \)** **Step 1:** Set up the equation from the proportion: \[ \frac{x + 2}{\frac{1}{2}} = 2 \] **Step 2:** Multiply both sides by \( \frac{1}{2} \) to isolate \( x + 2 \): \[ x + 2 = 2 \times \frac{1}{2} \] \[ x + 2 = 1 \] **Step 3:** Subtract 2 from both sides to solve for \( x \): \[ x = 1 - 2 \] \[ x = -1 \] --- ### **f) \( \frac{x - 1}{4} = \frac{3}{5} \)** **Step 1:** Set up the equation from the proportion: \[ \frac{x - 1}{4} = \frac{3}{5} \] **Step 2:** Cross-multiply to eliminate the fractions: \[ 5(x - 1) = 3 \times 4 \] \[ 5x - 5 = 12 \] **Step 3:** Add 5 to both sides: \[ 5x = 17 \] **Step 4:** Divide both sides by 5 to solve for \( x \): \[ x = \frac{17}{5} = 3.4 \] --- ### **Summary of Solutions:** - **d)** \( x = \frac{109}{150} \approx 0.727 \) - **e)** \( x = -1 \) - **f)** \( x = \frac{17}{5} = 3.4 \)