One Step Equations

One step equations are algebraic equations that can be solved in one step only. Such equations can be solved in just one step by adding, subtracting, multiplying, or dividing. To solve one-step equations, we apply the inverse of the fundamental operation of whatever operation is already applied to the variable. For example, if a constant is added to the variable, we subtract it to solve the one-step equation.

This article will discuss the concept of one-step equations and we will learn how to solve them step-wise. We shall solve various examples to understand the method of solving one step equations in a better way.

One step equations are algebraic equations that can be solved in just one step. We determine the value of the variable involved to solve such equations. We can linear, quadratic, as well as cubic one-step equations. We have different types of one step equations depending upon the types of coefficients and constant terms involved such as:

• One step equations with integers
• One step equations with fractions
• One step equations with decimals

Some of the examples of one step equations are:

• 2x = 7
• y - 7 = 6
• x² = 16
• a³ = -8
• x/5 = -10
• 4 + y = 9

Now that we have understood the meaning of one step equations, let us go through the process of solving one-step equations step-wise. The inverse operations pair-wise are addition and subtraction, and division and multiplication. Given below are the steps that help us in solving one step equations:

• Step 1: Understand and evaluate the one step equation.
• Step 2: Determine the operation applied to the variable.
• Step 3: Identify the inverse operation of the operation applied to the variable.
• Step 4: If the variable is multiplied by a number, divide both sides of the equation by the same number to isolate the variable. (If the variable is divided by a number, multiply both sides of the equation by the same number.)
• Step 5: If a number is added to the variable, then subtract the same number from both sides of the equation to isolate the variable. (If a number is subtracted from the variable, then add the same number to both sides of the equation to isolate the variable.)

In the above section, we went through the steps to solve one step equations. Let us now solve a few examples to understand the application of the given steps to solve one-step equations. We will consider equations where different operations are applied to the variable to understand the concept in a better way.

Example 1: Solve one step equation x - 7 = 10.

Solution: We have the equation x - 7 = 10. Since 7 is subtracted from the variable x, we will add (inverse of subtraction) 7 to both sides of the equation.

x - 7 + 7 = 10 + 7

⇒ x = 17

Example 2: Find the value of the variable: 4x = 16.

Solution: The one step equation is 4x = 16. Since 4 is multiplied by the variable x, we divide (inverse of multiplication) both sides of the equation by 4.

4x ÷ 4 = 16 ÷ 4

⇒ x = 4

Example 3: Solve the one step quadratic equation x² = 36.

Solution: We have x² = 36. Taking square root on both sides of the equation, we have

x = 6, -6

Important Notes on One Step Equations

• One step equations are equations in algebra that can be solved in only one step.
• The most common one step equations are linear algebraic equations.
• One step equations involving fractions are called one step equations with fractions.

☛ Related Articles:

• Two Step Equations
• Polynomials
• Variables, Constants, and Expressions

What are One Step Equations in Algebra?

One step equations are algebraic equations that can be solved in one step only. Such equations can be solved in just one step by adding, subtracting, multiplying, or dividing.

How to Solve One Step Equations?

To solve one-step equations, we apply the inverse of the fundamental operation of whatever operation is already applied to the variable. For example, if a constant is added to the variable, we subtract it to solve the one-step equation.

What are the Steps to Solve One-Step Equations?

Given below are the steps that help us in solving one step equations:

• Step 1: Understand and evaluate the one step equation.
• Step 2: Determine the operation applied to the variable.
• Step 3: Identify the inverse operation of the operation applied to the variable.
• Step 4: If the variable is multiplied by a number, divide both sides of the equation by the same number to isolate the variable. (If the variable is divided by a number, multiply both sides of the equation by the same number.)
• Step 5: If a number is added to the variable, then subtract the same number from both sides of the equation to isolate the variable. (If a number is subtracted from the variable, then add the same number to both sides of the equation to isolate the variable.)

What is a One Step Equation with Integers?

Algebraic equations involving integers as coefficients and constant terms that can be solved in just one step are called one step equations with integers.

What is the Difference Between One Step Equations and Two Step Equations?

One-step equations are algebraic equations that can be solved in just one step. On the other hand, two-step equations are equations in algebra that are solved in exactly two steps.

How to Solve One Step Equations with Fractions?

Algebraic equations involving fractions as coefficients and constant terms that can be solved in just one step are called one step equations with fractions. To solve such equations, we add, subtract, multiply or divide the equation with an appropriate fraction to isolate the variable.