Multi-Step Equation

Definition

A multi-step equation is a mathematical equation that requires more than one operation to solve for the unknown variable. These 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 its value.

5 Must Know Facts For Your Next Test

1. Multi-step equations often involve variables and constants on both sides of the equation, requiring a series of steps to isolate the variable.
2. Combining like terms, using the distributive property, and applying inverse operations are common strategies for solving multi-step equations.
3. The order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), must be followed when solving multi-step equations.
4. Checking the solution by substituting the found value back into the original equation is an important step to ensure the answer is correct.
5. Multi-step equations can model real-world situations, such as calculating the cost of multiple items or determining the time it takes to complete a task.

Review Questions

• Explain the importance of the order of operations when solving multi-step equations.
  • The order of operations, or PEMDAS, is crucial when solving multi-step equations because it determines the sequence in which the different operations are performed. Failure to follow the correct order can lead to incorrect solutions, as the operations must be executed in the proper sequence to isolate the variable and find its value. Adhering to PEMDAS ensures that the equation is solved consistently and accurately, regardless of the number of steps involved.
• Describe the role of inverse operations in solving multi-step equations.
  • Inverse operations play a vital role in solving multi-step equations. Inverse operations, such as addition and subtraction or multiplication and division, are used to isolate the variable by undoing the operations performed on both sides of the equation. By applying the appropriate inverse operations in the correct order, the variable can be moved to one side of the equation, allowing the value to be determined. Understanding and correctly applying inverse operations is a key skill in solving multi-step equations efficiently and accurately.
• Analyze how multi-step equations can be used to model real-world situations.
  • Multi-step equations can be used to model a wide range of real-world scenarios, as they allow for the representation of complex relationships between variables and constants. For example, a multi-step equation could be used to calculate the total cost of purchasing multiple items with different prices, or to determine the time required to complete a task given various factors. By setting up the equation to reflect the specific details of the situation, the unknown variable can be isolated and solved for, providing valuable insights and solutions to real-world problems. The ability to translate real-world situations into multi-step equations is a crucial skill in applied mathematics and problem-solving.

Related terms

Variable:

A symbol, usually a letter, that represents an unknown quantity in an equation.

Constant:

A fixed value in an equation that does not change.

Inverse Operations:

Operations that undo each other, such as addition and subtraction or multiplication and division, used to isolate the variable in an equation.