key term - Multi-Step Equation

Definition

A multi-step equation is a linear equation that requires more than one operation to isolate the variable and find the solution. These equations involve a series of steps, such as combining like terms, using the distributive property, or applying inverse operations, to get the variable by itself on one side of the equation.

5 Must Know Facts For Your Next Test

1. Multi-step equations often involve a combination of addition, subtraction, multiplication, and division to isolate the variable.
2. Proper order of operations, such as PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction), must be followed when solving multi-step equations.
3. Variables on both sides of the equation must be isolated by performing inverse operations on each side to find the solution.
4. Simplifying expressions by combining like terms is a crucial step in solving multi-step equations.
5. The solution to a multi-step equation is the value of the variable that makes the equation true.

Review Questions

• Explain the general strategy for solving a multi-step linear equation.
  • The general strategy for solving a multi-step linear equation involves a series of steps to isolate the variable. First, combine like terms on each side of the equation. Next, use inverse operations, such as addition and subtraction or multiplication and division, to isolate the variable. This may require applying the distributive property or other algebraic techniques. Finally, simplify the equation to find the value of the variable that makes the equation true.
• Describe how the order of operations (PEMDAS) is applied when solving a multi-step equation.
  • When solving a multi-step equation, the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction) must be followed to ensure the correct solution. This means that any operations within parentheses or exponents must be performed first, followed by multiplication and division from left to right, and then addition and subtraction from left to right. Adhering to this order is crucial for isolating the variable and finding the correct value that satisfies the equation.
• Analyze the role of combining like terms in the process of solving a multi-step equation.
  • Combining like terms is a critical step in solving multi-step equations. By combining the coefficients of variables with the same variable, the equation can be simplified, making it easier to isolate the variable and perform the necessary inverse operations. This step reduces the complexity of the equation and allows for more efficient problem-solving. Failing to combine like terms can lead to mistakes and make the equation more difficult to solve, so it is an essential skill to master when working with multi-step equations.

Related terms

Linear Equation:

An equation in which the variable appears only to the first power and the graph of the equation is a straight line.

Inverse Operations:

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

Combining Like Terms:

The process of adding or subtracting the coefficients of variables with the same variable.