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In acidic solutions, you have an excess of H+ which can be used along with H2O to balance H and O in the half reactions. In basic solutions, you have excess OH- which you would use to balance the half reactions. This is necessary to make sure that the charges and elements are balanced in the redox reactions.
When a redox reaction takes place in an acidic or basic solution, there would be an excess of H+ or OH- ions respectively. You need to use H+ to balance the half reactions in acidic solutions, and OH- to balance the half reactions in basic solutions. Also be sure to balance charges on both sides of the equations also by adding electrons to the appropriate sides of the half reactions.
The only difference when balancing a redox reaction in a basic solution compared to an acidic solution is that in basic solution, you would have to do the extra step of canceling the H+ with the OH- at the end (everything else is the same).
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