Solving Two-step Equations

In simple terms, the two-step equations are the ones that can be solved within two steps only. They are easy to solve since there is no one variable, either x or y. However, in these equations, we perform operations on both sides simultaneously. 

In this article, you will find brief information on the concept of two-step equations in Maths, a thorough explanation of linear equations, examples of two-step equations, and so on. So, let us start by describing the two-step equations in the Maths study material.

What are two-step equations? 

As the name suggests, the two-step equation can be solved in only two steps. It means that the final variable’s value can be extracted within two steps only. Note that the two-step equations are algebraic. Generally, these equations are represented as ax + b = c, where a, b, c are real numbers. Here are some common examples of two-step equations – 

• (2/3)z – 12 = 10
• 0.3y + 5 = 1
• 2x + 3 = 7

What are linear equations? 

A linear equation is often referred to as an equation with the highest degree of power of one variable. In other words, no variable has an exponent of more than one in a linear equation. In a graph, a linear equation constantly forms a straight line. Hence, it is named the linear equation. 

A linear equation in which only one variable is present, for example, Mx+N=0, where M and N are constant, and x is a variable. A linear equation in which two variables are present, for example, Mx+Ny=O, where M, N, and O are constant and x and y are variables. 

Steps to solve a two-step equation 

It is easy to solve the two-step equation as it is not as complicated and involves only two steps compared to other equations. It can be solved by isolating the variable on one side whereas other values on the other side. Here are steps to solve the two-step equation –

1. The first step is to simplify each side if required.
2. The next step is to use addition or subtraction properties to move the variable term to one side and all other terms to the other side.
3. The next step is to use multiplication or division for determining the variable value in a two-step equation.
4. The last step is to check the solution.

Now, let us solve an example following the steps mentioned above.

Example: Solve 6x – 32 = 8 – 2x

Solution

two step equation: 6x – 32 = 8 – 2x

Step 1: transfer variables to the one side of the equation

 6x + 2x = 8 + 32

Step 2: solve by adding or subtracting:

6x + 2x = 8 + 32

8x = 40

Step 3: divide the equation with 8 into both sides

8x = 40

8x/8 = 40/8

x = 5

Step 4: verify the answer by putting the value of x in a two step equation: 

6x – 32 = 8 – 2x

6*5 – 32 = 8 – 2*5

30 – 32 = 8 – 10

-2 = -2

The left-hand side is equal to the right-hand side; hence, the x we get on solving the equation is correct.

Hints in a two-step equation 

• The outcome of a two-step equation cannot be changed if the same number is subtracted, added, divided, or multiplied into both sides of the equation.
• The value of the variable generating a two-step equation valid is named the solution or root of the two-step equation. 
• The graph of a two-step equation in one or two variables constantly forms a straight line.

Golden rules for solving two-step equations 

The best way to acquire accurate results while solving the two-step equations is to solve both sides simultaneously. For isolating the variable on the one side of the equation for determining its value, the first step is to either add or sub on both sides of the equation. Then, multiply and divide on the side of the equation to get the final answer. 

• Simplify each side of the equation 
• Make sure you remove the constant first by adding or subtracting the number. 
• Do not forget to verify the solution at the end. 

Conclusion 

With this, we come to an end to solving two-step equations. As the name suggests, the two-step equation can be solved in only two steps with utmost ease. It means that the value of the final variable can be extracted within two steps only. These equations are algebraic. 

In this article describing solving two-step equations, we studied the concept of solving two-step equations and linear equations in length. We covered several other topics, such as Steps to solve two-step equations, golden rules of solving two-step equations, and other related topics. We hope this study material helped you better understand solving two-step equations.