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Equations with multiple terms with the same variable contain like terms. Like terms have the same variable and can be combined through addition or subtraction of their coefficients. In the example 11z - 4z + 2z = 27, the like terms 11z, 4z, and 2z can be combined to get 9z. Therefore, the equation becomes 9z = 27, and solving for z gives z = 3. Checking this solution by substituting z = 3 back into the original equation results in 27, confirming the solution.