Solve the equation:
(i) `-8le5x-3lt7`
(ii) `2le3x-4le5`
(iii) `-2le4-(7x)/(2)le18`.

Answer

Let's solve the given inequalities step by step.

### (i) Solve the inequality: `-8 ≤ 5x - 3 < 7`

1. **Break it into two parts:**
- First part: `-8 ≤ 5x - 3`
- Second part: `5x - 3 < 7`

2. **Solve the first part:**
- Start with `-8 ≤ 5x - 3`
- Add 3 to both sides:
\[ -8 + 3 ≤ 5x \implies -5 ≤ 5x \]
- Divide by 5:
\[ -1 ≤ x \implies x ≥ -1 \]

3. **Solve the second part:**
- Start with `5x - 3 < 7`
- Add 3 to both sides:
\[ 5x < 7 + 3 \implies 5x < 10 \]
- Divide by 5:
\[ x < 2 \]

4. **Combine the results:**
- From the first part, we have \( x ≥ -1 \)
- From the second part, we have \( x < 2 \)
- Therefore, the solution is:
\[ -1 ≤ x < 2 \]

### (ii) Solve the inequality: `2 ≤ 3x - 4 ≤ 5`

1. **Break it into two parts:**
- First part: `2 ≤ 3x - 4`
- Second part: `3x - 4 ≤ 5`

2. **Solve the first part:**
- Start with `2 ≤ 3x - 4`
- Add 4 to both sides:
\[ 2 + 4 ≤ 3x \implies 6 ≤ 3x \]
- Divide by 3:
\[ 2 ≤ x \implies x ≥ 2 \]

3. **Solve the second part:**
- Start with `3x - 4 ≤ 5`
- Add 4 to both sides:
\[ 3x ≤ 5 + 4 \implies 3x ≤ 9 \]
- Divide by 3:
\[ x ≤ 3 \]

4. **Combine the results:**
- From the first part, we have \( x ≥ 2 \)
- From the second part, we have \( x ≤ 3 \)
- Therefore, the solution is:
\[ 2 ≤ x ≤ 3 \]

### (iii) Solve the inequality: `-2 ≤ 4 - (7x)/2 ≤ 18`

1. **Break it into two parts:**
- First part: `-2 ≤ 4 - (7x)/2`
- Second part: `4 - (7x)/2 ≤ 18`

2. **Solve the first part:**
- Start with `-2 ≤ 4 - (7x)/2`
- Subtract 4 from both sides:
\[ -2 - 4 ≤ - (7x)/2 \implies -6 ≤ - (7x)/2 \]
- Multiply by -2 (remember to reverse the inequality):
\[ 12 ≥ 7x \implies x ≤ \frac{12}{7} \]

3. **Solve the second part:**
- Start with `4 - (7x)/2 ≤ 18`
- Subtract 4 from both sides:
\[ - (7x)/2 ≤ 18 - 4 \implies - (7x)/2 ≤ 14 \]
- Multiply by -2 (remember to reverse the inequality):
\[ 7x ≥ -28 \implies x ≥ -4 \]

4. **Combine the results:**
- From the first part, we have \( x ≤ \frac{12}{7} \)
- From the second part, we have \( x ≥ -4 \)
- Therefore, the solution is:
\[ -4 ≤ x ≤ \frac{12}{7} \]

### Final Solutions:
1. **(i)** \( -1 ≤ x < 2 \)
2. **(ii)** \( 2 ≤ x ≤ 3 \)
3. **(iii)** \( -4 ≤ x ≤ \frac{12}{7} \)