Two-Step Equations
Two step equations are equations that can be solved within exactly two steps. Two step equations are extremely easy to solve. As the name suggests, two step equations take only two steps to solve. These equations are just a little complicated than the one step equations. While solving a two step equation, we need to perform the operation on both sides of the equals to sign.
In this article, we will understand the meaning of two step equations with integers, decimals, and fractions, how to solve them, the golden rule to solve two step equations along with some examples for a better understanding.
| 1. | What are Two Step Equations? |
| 2. | Solving Two Step Equations |
| 3. | Two Step Equations with Decimals and Fractions |
| 4. | Golden Rule to Solve Two Step Equations |
| 5. | FAQs on Two Step Equations |
What are Two Step Equations?
Two step equations are algebraic problems that take just two steps to solve. The two step equation is a linear equation in one variable. While performing an operation for solving a two step equation, we need to perform the same operation on both sides of the equation. We isolate the variable on one side of the equation to determine its value.
Two Step Equations Definition
Two step equations are algebraic equations and are the equations that can be solved in exactly two steps and gives the final value of the variable in two steps. Generally, two step equations are of the form ax + b = c, where a, b, c are real numbers. A few examples of two step equations are:
- 2x + 3 = 7
- 0.3y + 5 = 1
- (2/3)z - 12 = 10
Solving Two Step Equations
Two step equations are very easy to solve. It includes just one extra step as compared to one-step equations to solve. We can solve a two-step equation by isolating the variable (usually represented by an alphabet or letter) on one side of the equation and all other values on the other side. The general two steps to solve the two-step equations are:
- Step 1: Addition and subtraction to isolate the variable.
- Step 2: Multiplication or division to determine the value of the variable.
Let us consider a few examples and solve two-step equations to understand the concept of solving two-step equations.
Example 1: Solve the equation 2x + 6 = 12.
To solve the two step equation 2x + 6 = 12, we need to determine the value of x. Let us solve it step-wise.
Step 1: Subtract -6 from both sides of the equation to isolate the variable x.
2x + 6 - 6 = 12 - 6
⇒ 2x = 6
Step 2: Divide both sides of the equation by 2 to solve for x.
2x/2 = 6/2
⇒ x = 3
Hence, we have solved the equation 2x + 3 = 12 in just two steps.
Thus the two-step equation can be easily solved in a sequence of steps, as presented above.
Two-Step Equations with Decimals and Fractions
Two step equations that have decimals and fractions as the coefficient of the variable and constant term are said to be two step equations with decimals and fractions. A few examples of two step equations with fractions and decimals are:
- 0.3 x + 2/3 = 1
- 3x - 0.5 = 1.2
- (1/3) x + 4/5 = 3/4
These equations are solved in the same manner as the general two steps equations and the same steps are followed to determine the value of the variable.
Golden Rule to Solve Two Step Equations
The golden rule to solve two step equations is to perform all operations simultaneously on both sides of the equation. To isolate the variable on one side of the equation and to determine its value, we first add or subtract on both sides of the equation and then multiply or divide on both sides to get the final solution of the two step equation.
Important Notes on Two Step Equations
- Remove the parentheses and combine like terms to simplify each side of the two-step equation.
- Always remove the constant first by adding or subtracting the appropriate number.
- Always verify the solution in the end.
Topics Related to Two Step Equations
FAQs on Two Step Equations
What are Two Step Equations in Algebra?
Two step equations are algebraic equations that take just two steps to solve.First, the variable is isolated by adding or subtracting a numeric value on both sides of the equation. Secondly, the value of the variable is computed by multiplying or dividing the variable by an appropriate number.
What are the Steps to Solve Two Step Equations?
The general two steps to solve two step equations are:
- Step 1: Simplify the given equation by removing all brackets and parenthesis:
- Step 2: Add or subtract to isolate the variable.
- Step 2: Multiply or divide to determine the value of the variable.
- Step: Verify the answer by substituting it in the given equation.
How to Solve Two Step Equations?
Two step equations can be solved by following two quick steps:
- Step 1: Add or subtract numbers on either sides, to isolate the variable.
- Step 2: Multiply or divide to determine the value of the variable.
IS Two Step Equation the Same as A Multi-Step Equation?
Two-step equation can also be called a multi-step equation since it involves more than one step. And a multi-step equation can have two or more steps, in the process of solving the equation.
What is the Difference Between One Step and Two Step Equations?
One step equations take just one step to solve whereas two steps equations take two steps to get to the solution. Two-step equations include just one extra step as compared to one step equations to solve.
What is the Goal of Solving Two Step Equations?
The goal of solving two step equations is to isolate the variable and determine the value of the variable. And in the end, the variable should satisfy the given two step equation.