When an Account is marked Inactive__c = true, automatically close all related open Cases and mark open Opportunities as Closed Lost.

trigger AccountTrigger on Account (after update) {
    Set<Id> inactive = new Set<Id>();
    for (Account a : Trigger.new) if (a.Inactive__c && !Trigger.oldMap.get(a.Id).Inactive__c) inactive.add(a.Id);
    if (inactive.isEmpty()) return;
    List<Case> cases = [SELECT Id FROM Case WHERE AccountId IN :inactive AND IsClosed = false];
    for (Case c : cases) c.Status = 'Closed';
    List<Opportunity> opps = [SELECT Id FROM Opportunity WHERE AccountId IN :inactive AND IsClosed = false];
    for (Opportunity o : opps) o.StageName = 'Closed Lost';
    update cases; update opps;
}