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➕pre-algebra review

Multi-Step Equations

Written by the Fiveable Content Team • Last updated September 2025
Written by the Fiveable Content Team • Last updated September 2025

Definition

Multi-step equations are mathematical equations that require more than one operation to solve for the unknown variable. These types of equations involve a sequence of steps, such as combining like terms, using the distributive property, or applying inverse operations, to isolate the variable and find the solution.

5 Must Know Facts For Your Next Test

  1. Multi-step equations can involve a combination of addition, subtraction, multiplication, and division operations.
  2. Solving multi-step equations often requires the use of inverse operations to isolate the variable.
  3. The distributive property is commonly used in multi-step equations to simplify expressions with parentheses.
  4. Combining like terms is an essential step in solving multi-step equations to reduce the number of terms.
  5. The solution to a multi-step equation can be a rational number, including decimals and fractions.

Review Questions

  • Explain the importance of using inverse operations when solving multi-step equations.
    • Inverse operations are crucial when solving multi-step equations because they allow you to isolate the variable by undoing the various operations performed on it. For example, if an equation involves adding a number to the variable and then multiplying the result by another number, you would need to use the inverse operations of division and subtraction to isolate the variable and find the solution.
  • Describe how the distributive property can be used to simplify multi-step equations with parentheses.
    • The distributive property can be used to simplify multi-step equations with parentheses by distributing the operation outside the parentheses to each term inside. This can help combine like terms and reduce the number of steps required to solve the equation. For instance, in the equation $5(2x + 3) = 10x + 15$, the distributive property is used to multiply each term inside the parentheses by the 5 outside, resulting in a simpler equation to solve.
  • Analyze the role of combining like terms in the process of solving multi-step equations.
    • Combining like terms is a crucial step in solving multi-step equations because it helps to simplify the equation and reduce the number of terms that need to be manipulated. By combining terms with the same variable and exponent, you can more easily apply inverse operations and isolate the variable. This step also helps to minimize the chances of making computational errors during the equation-solving process. Effectively combining like terms is a key skill for successfully navigating multi-step equations.