102 LearnersLast updated on July 13th, 2025
Linear Equation in One Variable
A linear equation is a simple way to express a mathematical relationship. In a linear equation, ‘x’ represents the unknown quantity. We will learn more about linear equations in one variable in this article.
What is Linear Equation in One Variable?
In a linear equation, each variable has a degree of exactly 1. A linear equation in one variable contains only a variable and results in just one solution. When we draw the linear equation, it makes a straight line. Depending on the equation, the graph can be a slanted, horizontal, or vertical line. The general form is ax + b = 0, where x is an unknown variable and a and b are constants.
For example, adding 7 to an unknown number gives 25.
Here we have only one unknown variable.
x + 7 = 25
Difference Between Linear Equation in One Variable vs Non-Linear Equations
|
Linear Equation |
Non-Linear Equation |
|
It forms a straight line when plotted on a graph. |
Non-linear equations create curves or other shapes on graphs. |
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A linear equation does not have powers or exponents. |
These equations include higher powers like squares, fractions, and other powers like x2, y2, etc. |
|
The highest degree of the linear equation is 1. |
A non-linear equation has the highest degree of 2 or greater. |
|
Linear equations are used for simple problems like finding speed, making budgets, or calculating total cost based on quantity. |
Non-linear equations are used in physics, geometry, etc. |
|
Example: 3x + 2 = 8 |
Example: x2 + y2 = 9 |
How to Solve Linear Equations in One Variable?
A linear equation in one variable has only one variable, does not include squared terms or similar higher powers, and the highest degree is 1. The standard form of a linear equation is ax + b = 0. Where x is the unknown variable, a is the coefficient, and b is the constant. A linear equation in one variable can be solved using the following methods.
- Balancing Method
- Transposition Method
Balancing Method
In the balancing method, the equation is like a weighing scale; both sides must stay equal. To solve an equation, we must do the same thing to both sides:
- Add the same number on both sides.
- Subtract the same number from both sides
- Multiply or divide both sides by the same non-zero number to find the value of a variable.
- Move the term to the other side by changing its sign.
Example: x - 3 = 7
Add 3 to both sides to eliminate the -3.
x - 3 + 3 = 7 + 3
x = 10
Transposition Method
The transposition means moving a term from one side to the other side by changing its sign.
Example: x + 5 = 12
Move 5 to the other side so it will become -5.
x = 12 - 5
x = 7
Solving Equations With Variables on One Side
Some equations have variables on one side to solve these, move the number to the other side, and use the opposite operations to isolate the variable.
Example: 2x - 4 = 10
Add 4 to both sides of the equation,
2x - 4 = 10 + 4
2x = 14
Divide both sides by 2
x = 7
Real Life Applications of Linear Equation in One Variable
Linear equations in one variable are useful when only one unknown quantity needs to be found. Here are some real-life applications of linear equations.
- Finance and Budgeting: It is used to track expenses and income, calculate savings, or planning for future spending. If your income is fixed and expenses vary, a linear equation helps you to solve for what you can afford and how much you are left with.
- Shopping and Retail: Retailers use linear equations to find final prices after applying discounts or adding taxes.
- Education and Exams: Linear equations help us determine the required scores, averages, or marks needed to improve grades.
- Salaries: They are used to calculate the total pay, including bonus, overtime, and deductions while calculating salaries.
Common Mistakes and How To Avoid Them in Linear Equations in One Variable
Students make mistakes when solving a linear equation in one variable. Here are some of the common mistakes and the ways to avoid them.
Mistake 1
Not changing the sign
Not changing the signs when moving a number from one side to the other side makes a mistake. Always change the sign when moving a term across the equal sign. For example, In x + 2 = 10, when moving 2 to the other side, it will change its sign and become negative, so the equation becomes x = 10 - 2.
Mistake 2
Not applying the operations to all terms
When multiplying 2(x + 3), multiplying 2 only by x and writing it as 2x + 3 is incorrect. Apply the distributive property to each term inside the brackets, and multiply 2 by every term inside the brackets. For example: 2(x + 3) = 2x + 6.
Mistake 3
Adding instead of dividing
Solving 3x = 18 by writing x = 18 + 3 = 21 is incorrect. When a number is multiplied by the variable, you need to divide both sides by that number and move it to the other side.
Mistake 4
Solving an equation with zero incorrectly
If an equation has a term like 0x = 5, it’s incorrect to write it as x = 5. Since 0x is always 0, and 0 can never equal 5, such equations have no solution.
Mistake 5
Incorrect solution
When both sides of an equation have the same terms, some students mistakenly try to solve it. But if an equation has both sides equal, the equation is an identity, and is true for all values of the variable. This means it has infinitely many solutions.
Solved Examples of Linear Equation in One Variable
Problem 1
Solve 2x + 5 = 13
x = 4
Explanation
Subtract 5 from both sides
2x + 5 = 13
2x + 5 - 5 = 13 - 5
2x = 8
Divide both sides by 2
x = 4
Problem 2
Solve 3x - 7 = 2x + 1
x = 8
Explanation
Move all the x terms to one side
3x - 7 = 2x + 1
3x - 2x = 1 + 7
x = 8
Problem 3
Solve x/3 + 2 = 5
x = 9
Explanation
Subtract 2 from both sides
x/3 + 2 = 5
x/3 + 2 - 2 = 5 - 2
x/3 = 3
Multiply both sides by 3
x = 9
Problem 4
Solve 5(x - 2) = 3(x + 4)
x = 11
Explanation
Expand both sides
5(x - 2) = 3(x + 4)
5x - 10 = 3x + 12
Move x terms to one side
5x - 3x = 12 + 10
2x = 22
Divide both sides by 2,
x = 11
Problem 5
Solve -4x + 9 = 5
x = 1
Explanation
Subtract 9 from both sides
-4x + 9 = 5
-4x = -4
Divide by -4
x = 1
FAQs on Linear Equation in One Variable
1.What is a linear equation in one variable?
2.Why is it called a linear equation?
3.What types of solutions do linear equations have?
4.What is the difference between an equation and an expression?
5.Can a linear equation include powers other than 1?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Linear Equation in One Variable?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Linear Equation in One Variable?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
