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It affects the way you balance the equations. For a reaction in an acidic soln, you would balance the O's in the half-reactions using H2O and then balance the H's using H+ ions. For a reaction in a basic soln, you would balance the O's in the half-reactions using H2O and then, to balance the H's, add H2O to the side without H2O and then add OH- to the side that already had an H2O from your previous step. Otherwise, the steps to balance the redox reaction are the same whether acidic or basic.
When dealing with acids and bases, the balancing of equations would be effected. This is based on the H+ present in acid and OH- present in bases which needs to be accounted for in the reaction.
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