In the general plan for balancing redox equations, when a reaction takes place in basic solution, you will need to add

Answer is: add hydroxide ions (OH⁻).

For example unbalanced chemical reaction:

H₂O₂ (aq) + Cl₂O₇ (aq) → ClO₂⁻ (aq) + O₂ (g).

Reduction half reaction: 6H ⁺ + Cl₂O₇ → 2ClO₂⁻ + 3H₂O.

Oxidation half reaction: H ₂O₂ → O₂ + 2H⁺ + 2e⁻ / * 4; 4H₂O₂ → 4O₂ + 8H⁺ + 2e⁻

Sum: 6H ⁺ + Cl₂O₇ + 4H₂O₂ → 4O₂ + 8H⁺ + 2ClO₂⁻ + 3H₂O;

Cl ₂O₇ + 4H₂O₂ → 4O₂ + 2H⁺ + 2ClO₂⁻ + 3H₂O

Add 2 OH ⁻: 2OH⁻ + Cl₂O₇ + 4H₂O₂ + → 4O₂ + 2ClO₂⁻ + 5H₂O.

Balanced chemical reaction: 4H ₂O₂ + Cl₂O₇ + 2OH⁻→ 2ClO₂⁻ + 4O₂ + 5H₂O.