Maths problem: I think my (b) (ii )answer is wrong, please teach me how to do, thanks?

Question：
If -3 ≤ x ≤ -1, find the range of the values of z when z = 1/(1 - x).
🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘🔘
Solution：
Method 1：
∵ -3 ≤ x ≤ -1
-(-1) ≤ -x ≤ -(-3)
1 ≤ -x ≤ 3
1 + 1 ≤ - x + 1 ≤ 3 + 1
2 ≤ 1 - x ≤ 4
1/4 ≤ 1/(1 - x) ≤ 1/2
∴ 1/4 ≤ z ≤ 1/2

Method 2：
z = 1/(1 - x)
......
x = (z - 1)/z
∴ -3 ≤ (z - 1)/z ≤ -1
......
1 ≤ 4z ≤ 1 + 2z

Since 1 ≤ 4z, z ≥ 1/4.
Since 4z ≤ 1 + 2z, 2z ≤ 1, z ≤ 1/2.
∴ Combine two cases, 1/4 ≤ z ≤ 1/2.