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How to Use Inverse Operations to Solve Two-Step Equations

two-step equation example: Person writing a mathematical equation on a blackboard

A two-step equation is pretty self-explanatory: It's an equation with two different elements, a variable and a positive or negative constant, that can be solved in two steps. To solve two-step equations, you have to inverse the order of operations to determine which part of the equation to solve first.

What Is the Order of Operations?

The order of operations is a rule that establishes the sequence in which the operations of a multi-step equation should be solved. This rule goes by a process called PEMDAS, which established the following order for solving an equation:

P: Parentheses ( )

E: Exponents ^

M: Multiplication ×

D: Division ÷

A: Addition +

S: Subtraction ⁻

Solving Two-Step Equation Examples With Inverse Operations

Since the purpose of solving two-step equations is to determine the value of x, the multiplication or division of the coefficient attached to x must be the last step. Because of this, you must use inverse operations to solve two-step equations. This means adding and subtracting first, then multiplying and dividing. Adding and subtracting are usually the last steps in the order of operations, while multiplication and division are early steps.

Let's use this inverse order to solve for variable x in this two-step equation example:

two-step equation example using inverse order

Using inverse operations, the first step to solving this two-step equation example is to subtract 13 from 37. The left-hand side will now equal 4x and the right side will equal 24

Equation showing the left-hand side value is 4x and right side is 24

Let's solve for x by dividing by 4. The value of the variable x will now be…

Equation showing the value of the variable x is 6

How to Solve Two-Step Equations

Two-step equations are simple but have one critical rule — you must use the inverse order of operations. When you're able to (partly) put aside what you've learned about PEMDAS and the order of operations, you can solve for the variable of any two-step equation.

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