Solving Equations with Variables on Both Sides Calculator is a free online tool that displays the value of the unknown variable. BYJU’S online calculator tool makes calculations faster and easier. The unknown value of the given equation is displayed in a fraction of seconds.
The procedure to use this calculator is as follows:
Step 1: Enter the equation in “Solve the Equation” field
Step 2: Click the button “Solve” to get the output
Step 3: The unknown value of the given equation will be displayed in a new window
Equation Definition
In Mathematics, an equation is an expression that equals two values. It consists of two expressions separated by an equal sign “=”. If an expression is represented using equal sign, the value of one side should be equal to the value on the other side. Most of the linear equation contains one or two variables. Let us consider an example,
Let x be an unknown value
x = 20 +15
We can say that the value of x should satisfy the value 35. Because, 20+ 15 = 35. The process of finding the unknown value in an equation is known as “Solving the Equation”.
Standard Form
The standard form used to represent the equation is given below:
Ax + By = C
Here, x and y are the two unknown values (i.e., variable)
Frequently Asked Questions on Solving Equations With Variables on Both Sides Calculator
5x+2=12 The different types of equations are:Solve the given equation: 5x + 2 = 12
5x=12-2
x=10/5
x=2What are the different types of equations?
Write the classification of linear equation with examples.
The three different classifications of linear equations are:
- Equation with one variable
Example: 5x =10
- Equation with two variables
Example: 2x + 4y = 10
- Equation with three variables
Example: x + y + z = 15
The following figure shows how to solve equations with variables on both sides. Scroll down the page for more examples and solutions.
Example:
Consider the equation x – 6 = –2x + 3.
To isolate the variable, we need to get all the variable terms to one side and the constant terms to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.
Solve x – 6 = –2x + 3
Solution:
Step 1: Get all the variable terms to one side and the constant terms to the other side.
x – 6 = –2x + 3
x – 6 + 2x + 6 = –2x + 3 + 2x + 6 (Add 2x & 6 to
both sides)
Step 2: Combine like terms
2x + x = 3 + 6
3x = 9
Step 3: Divide or multiply to isolate the variable
3x = 9 (Divide by 3)
x = 3
Check:
x – 6 = –2x + 3
3 – 6 = –2 • 3 + 3 (substitute x = 3 into the original equation)
–3 = –3
Example:
Consider the equation 6x – 4 = 3x + 2. To isolate the variable, we need to get all the variable terms to
one side and the constant terms to the other side. Next, we combine like terms and then isolate the variable by multiplying or dividing.
Solve 6x – 4 = 3x + 2
Solution:
Step 1: Get all the variable terms to one side and the constant terms to the other side.
6x – 4 = 3x + 2
6x – 4 – 3x + 4 = 3x + 2 – 3x + 4 (Subtract 3x & add 4 to both sides)
Step 2: Combine like terms
6x – 3x = 2 + 4
3x = 6
Step 3: Divide or multiply to isolate the variable
3x = 6 (Divide by 3)
x = 2
Check:
6x – 4 = 3x + 2 (substitute x = 2 into the original equation)
6 • 2 – 4 = 3 • 2 + 2
8 = 8
How to solve equations with variables on both sides of the equation?
Examples:
- 5x + 8 = 7x
- 4w + 8 = 6w – 4
- 6(g + 3) = – 2(g + 31)
- Show Video Lesson
Solving Equations with Variables on Both Sides
Step 1: Add and subtract terms to get the variables on one side and the
constants on the other.
Step 2: Multiply or divide to isolate the variable.
Examples:
- 2x + 7 = 4x – 7
- 3x + 19 = 3 – 5x
- Show Video Lesson
Equations With Variables on Both Sides
This requested video looks at solving equations with variables on both sides. It includes four examples.
Examples:
- x + 14.8 = 102 – 7x
- 5y – 2 = 28 – y
- 3 + 5m = 8m – 9
- 4 + 3x – 6 = 3x + 2 – x
- Show Video Lesson
How to use the distributive property to simplify equations with variables on both sides?
Examples:
- 3(x – 1) = 2(x + 3)
- z/6 = 2(z + 1)/9
- Show Video Lesson
Try the free
Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.