Write the following as intervals:
(i) `{x:x inR,-4ltxle6}`
(ii) `{x:x inR, -12ltxlt-10}`
(iii) `{x:x inR, 0lexlt7}`
(iv)`{x:x in R , 3lexle4}`.

Answer

To convert the given set notation into interval notation, we will follow a systematic approach for each part of the question.

### Step-by-Step Solution:

**(i)** For the set `{x: x ∈ R, -4 < x ≤ 6}`:
- The inequality states that x is greater than -4 (not including -4) and less than or equal to 6.
- In interval notation, this is represented as:
\[ (-4, 6] \]

**(ii)** For the set `{x: x ∈ R, -12 < x < -10}`:
- The inequality states that x is greater than -12 (not including -12) and less than -10 (not including -10).
- In interval notation, this is represented as:
\[ (-12, -10) \]

**(iii)** For the set `{x: x ∈ R, 0 ≤ x < 7}`:
- The inequality states that x is greater than or equal to 0 and less than 7 (not including 7).
- In interval notation, this is represented as:
\[ [0, 7) \]

**(iv)** For the set `{x: x ∈ R, 3 ≤ x ≤ 4}`:
- The inequality states that x is greater than or equal to 3 and less than or equal to 4.
- In interval notation, this is represented as:
\[ [3, 4] \]

### Final Answer:
1. (i) \((-4, 6]\)
2. (ii) \((-12, -10)\)
3. (iii) \([0, 7)\)
4. (iv) \([3, 4]\)