Step 1: Understanding peroxide ion bond order.
Peroxide ion is \(O_2^{2-}\). Its molecular orbital configuration gives a bond order of 1. This is because two extra electrons occupy antibonding orbitals, reducing bond order compared to oxygen molecule. So we take \(x = 1\).
Step 2: Understanding superoxide ion bond order.
Superoxide ion is \(O_2^{-}\). It has one extra electron compared to oxygen molecule. This reduces bond order slightly, giving bond order \(1.5\).
Step 3: Relating peroxide and superoxide bond orders.
We are given peroxide bond order as \(x = 1\). Superoxide bond order is \(1.5\), which is higher than peroxide.
Step 4: Expressing in terms of x.
Since peroxide bond order \(x = 1\), superoxide bond order becomes:
\[
\frac{3}{2}x
\]
Step 5: Final reasoning.
Thus, the bond order of superoxide ion is 1.5 times that of peroxide ion. This matches molecular orbital theory trends for oxygen species.
Final Answer:
\[
\boxed{\frac{3}{2}x}
\]