Two Step Equations
By If you’re a student of mathematics, you’ll know that solving equations is an essential part of the subject. Solving equations is like solving a puzzle, and two-step equations are an important type of equation that you’ll come across in your studies. In this blog, we’ll take you through solving two-step equations step by step, from the basics to more complex examples. By the end of this guide, you’ll have a good understanding of how to solve two-step equations, which will help you in your future math studies.
Before we begin, let’s start with a definition of two-step equations. A two-step equation is an algebraic equation that requires two steps to solve. The equation includes both an operation (addition, subtraction, multiplication or division) and a variable (a letter that represents a number). Here’s an example:
2x + 5 = 11
This equation includes both addition and multiplication operations, and the variable is represented by ‘x’. To solve this equation, we need to follow two steps:
Step 1: Subtract 5 from both sides of the equation
2x + 5 – 5 = 11 – 5
2x = 6
Step 2: Divide both sides of the equation by 2
2x/2 = 6/2
x = 3
Now that we’ve covered the basics, let’s move on to solving more complex two-step equations.
Step-by-Step Guide to Solving Two-Step Equations
Step 1: Identify the operations in the equation
The first step in solving a two-step equation is to identify the operations in the equation. Look for addition, subtraction, multiplication or division operations. It’s important to note that you need to apply the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction), when solving two-step equations.
Step 2: Undo the addition or subtraction
Once you’ve identified the operation, you need to undo it. If the operation is addition or subtraction, you need to undo it by using the opposite operation. For example, if the operation is addition, you need to subtract the same number from both sides of the equation. If the operation is subtraction, you need to add the same number to both sides of the equation.
Step 3: Undo the multiplication or division
If the operation in the equation is multiplication or division, you need to undo it by using the opposite operation. If the operation is multiplication, you need to divide both sides of the equation by the same number. If the operation is division, you need to multiply both sides of the equation by the same number.
Step 4: Simplify the equation
After undoing the operations, simplify the equation by combining like terms. Like terms are terms that have the same variable raised to the same power. For example, 2x and 5x are like terms because they both have ‘x’ raised to the first power.
Step 5: Solve for the variable
Once you’ve simplified the equation, you can solve for the variable by isolating it on one side of the equation. Remember that you need to apply the same operations to both sides of the equation to keep it balanced.
Let’s take a look at an example of a two-step equation to see these steps in action:
3x – 7 = 8
Step 1: Identify the operations in the equation
The operation in this equation is subtraction.
Step 2: Undo the subtraction
To undo the subtraction, we need to add 7 to both sides of the equation.
3x – 7 + 7 = 8 +
Step 3: Undo the multiplication
There is no multiplication in this equation.
Step 4: Simplify the equation
3x = 15
Step 5: Solve for the variable
To solve for the variable, we need to divide both sides of the equation by 3.
3x/3 = 15/3
x = 5
So the solution to the equation 3x – 7 = 8 is x = 5.
Now let’s move on to some more examples of two-step equations.
Example 1:
2y + 5 = 11
Step 1: Identify the operations in the equation
The operation in this equation is addition.
Step 2: Undo the addition
To undo the addition, we need to subtract 5 from both sides of the equation.
2y + 5 – 5 = 11 – 5
2y = 6
Step 3: Undo the multiplication
There is no multiplication in this equation.
Step 4: Simplify the equation
2y = 6
Step 5: Solve for the variable
To solve for the variable, we need to divide both sides of the equation by 2.
2y/2 = 6/2
y = 3
So the solution to the equation 2y + 5 = 11 is y = 3.
Example 2:
4a – 7 = 17
Step 1: Identify the operations in the equation
The operation in this equation is subtraction.
Step 2: Undo the subtraction
To undo the subtraction, we need to add 7 to both sides of the equation.
4a – 7 + 7 = 17 + 7
4a = 24
Step 3: Undo the multiplication
To undo the multiplication, we need to divide both sides of the equation by 4.
4a/4 = 24/4
a = 6
So the solution to the equation 4a – 7 = 17 is a = 6.
Example 3:
5x/2 + 1 = 7
Step 1: Identify the operations in the equation
The operations in this equation are division and addition.
Step 2: Undo the addition
To undo the addition, we need to subtract 1 from both sides of the equation.
5x/2 + 1 – 1 = 7 – 1
5x/2 = 6
Step 3: Undo the multiplication
To undo the division, we need to multiply both sides of the equation by 2.
2(5x/2) = 2(6)
5x = 12
Step 4: Simplify the equation
5x = 12
Step 5: Solve for the variable
To solve for the variable, we need to divide both sides of the equation by 5.
5x/5 = 12/5
x = 2.4
So the solution to the equation 5x/2 + 1 = 7 is x = 2.4.
FAQs
What is a two-step equation?
A two-step equation is an algebraic equation that requires two steps to solve. The equation includes both an operation (addition, subtraction, multiplication or division) and a variable (a letter that represents a number).
What are the steps to solve a two-step equation?
The steps to solve a two-step equation are as follows:
Step 1: Identify the operations in the equation
Step 2: Undo the addition or subtraction
Step 3: Undo the multiplication or division
Step 4: Simplify the equation
Step 5: Solve for the variable
What is the order of operations?
The order of operations is also known as PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. It’s the order in which you should perform mathematical operations when solving an equation.
Can a two-step equation have multiple solutions?
No, a two-step equation can only have one solution.
Can a two-step equation have no solution?
Yes, a two-step equation can have no solution if the equation is contradictory, meaning there’s no value that satisfies the equation.
What if the equation has fractions or decimals?
If the equation has fractions or decimals, you can use the same steps to solve it. However, you may need to perform additional steps to simplify the equation and get rid of the fractions or decimals.
What if there are variables on both sides of the equation?
If there are variables on both sides of the equation, you need to simplify the equation by combining like terms and then move all the variables to one side of the equation.
What if there are parentheses in the equation?
If there are parentheses in the equation, you need to use the distributive property to simplify the equation.
What if there are exponents in the equation?
If there are exponents in the equation, you need to use the rules of exponents to simplify the equation.
How can I check my answer?
To check your answer, you can substitute the value you found for the variable back into the original equation and see if both sides of the equation are equal.
