Solve the equation:
(i) `(3x-2)/(5)le(4x-3)/(2)`
(ii) `(2(x-1))/(5)le(3(2+x))/(7)`
(iii) `(3(x-2))/(5)le(5(2-x))/(3)`

Answer

Let's solve the given inequalities step by step.

### (i) Solve the inequality:
\[ \frac{3x - 2}{5} \leq \frac{4x - 3}{2} \]

**Step 1: Move all terms to one side.**
\[ \frac{3x - 2}{5} - \frac{4x - 3}{2} \leq 0 \]

**Step 2: Find a common denominator.**
The common denominator for 5 and 2 is 10. Rewrite the fractions:
\[ \frac{2(3x - 2)}{10} - \frac{5(4x - 3)}{10} \leq 0 \]

**Step 3: Simplify the expression.**
\[ \frac{6x - 4 - (20x - 15)}{10} \leq 0 \]
\[ \frac{6x - 4 - 20x + 15}{10} \leq 0 \]
\[ \frac{-14x + 11}{10} \leq 0 \]

**Step 4: Remove the denominator (since it is positive).**
\[ -14x + 11 \leq 0 \]

**Step 5: Solve for x.**
\[ -14x \leq -11 \implies x \geq \frac{11}{14} \]

**Final Answer for (i):**
\[ x \geq \frac{11}{14} \]