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485 LearnersLast updated on December 12, 2025
Equation
In mathematics, when we need to find the value of a variable, we can use an equation. This is called a mathematical equation, and it consists of two sides, the left-hand side (LHS) and right-hand side (RHS). An equal sign separates the LHS and the RHS of any equation.
What are Equations?
An equation is a mathematical statement that shows the equality of two expressions using an equals sign (=). It has a left-hand side (LHS) and a right-hand side (RHS), and both sides represent the same value.
Equations are used to find the value of unknown variables. If a mathematical statement does not contain an equals sign, it is not an equation; it is simply an expression.
| Statement | Statement |
| y = 8x - 9 | Yes |
| Y + x2 -8 | No |
| 3 + 2 = 7 - 2 | Yes |
| 3x2 + 5x - 2 = 0 | Yes |
Difference Between Expression & Equation
Although both expressions and equations are used in algebra, they differ from each other. The table below illustrates the differences between them.
| Expression | Equation |
| An expression can be written without an equal to sign. | An equation cannot be written without an equal sign. |
| A mathematical expression consists of one or more terms connected by operations, such as addition, subtraction, etc. | In an equation, two expressions are equal. These two expressions are represented using the = sign. |
| Example: \(x - y + 8\) | Example: \(2b + 4 = c + 6\) |
What are the Types of Equations?
Equations are categorized based on their degree, which is the highest power of the variable in the given equation. Learning about different types of equations will improve student's ability to solve problems related to this topic. Given below is a list and explanation of different types of equations:
- Linear Equation
- Quadratic Equation
- Cubic Equation
- Rational Equation
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Linear Equation
A linear equation is an equation in which the highest power (degree) of the variable is 1. Because the degree is one, these equations are also called first-degree equations. Linear equations can involve one, two, or more variables.
The general form of a linear equation in variables p and q can be written as:
ap + bq + c = 0,
where a and b are coefficients, and c is a constant. Here, the variables p and q each have degree 1.
Quadratic Equation
A quadratic equation is an equation in which the highest degree of the variable is 2. Because the degree is two, it is also called a second-degree equation. The general form of a quadratic equation in the variable m is:
\(am^2 + bm + c = 0\) where \(a ≠ 0\).
In the equation:
- \(m^2\) is the highest degree
- a and b are the coefficients
- c is the constant term
Cubic Equation
In cubic equations, one of the variables will have 3 as the highest degree. The general form of a cubic equation will be:
\(ax^3 + bx^2 + cx + d = 0\),
where
- x3 is the variable with the highest degree.
- a, b, and c are coefficients of \(x^3\), \(x^2\), and x respectively,
- and d is the constant.
Rational Equation
Equations containing a fraction, where the numerator or denominator or both contain a variable, are rational equations. The rational equation is:
\( \frac{b}{3} = a + \frac{c}{4} \)
What are the Parts of an Equation?
We know that an equation comprises LHS and RHS connected by the equal to sign. Apart from the LHS and RHS, an equation also includes the following components:
- Coefficient: A number that multiplies a variable
- Variable: A letter or symbol that represents a value
- Operator: Symbols like +, -, ×, to show different arithmetic operations
- Constant: A value that doesn't have any variable attached to it
Take a look at the expression given below:
\((3 × x) + 15 = 24\)
Here,
- LHS is 3x + 15 and RHS is 24.
- In 3x, 3 is the coefficient of the variable x.
- + is the operator.
- 15 and 24 are the constants.
How to Solve Equations?
An equation states that the left-hand side (LHS) equals the right-hand side (RHS). To solve an equation and find the value of an unknown variable, follow these steps:
- Separate variables and constants
- Then simplify both sides
- Isolate the variable by performing operations to move it to one side.
For example, solve the equation: 3x - 2 = 4
Moving the constant -2 to the RHS
3x = 4 + 2
Simplify the RHS:
3x = 6
Divide both sides by 3 to isolate x:
3x ÷ 3 = 6 ÷ 3
x = 2
Here, x = 2
Tips and Tricks to Master Equations
To make working with equations easier, quick and efficient, students can include these tips and tricks while practicing.
- Keep variables on one side: Always move all variables to one side and constants to the other for easy solving.
- Use inverse operations: Undo addition, subtraction, multiplication, or division step by step.
- Simplify before solving: Combine like terms and simplify fractions to avoid errors.
- Check your solution: Substitute your answer back into the equation to verify it.
- Stay organized: Write each step clearly to track your operations and prevent mistakes.
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Relate equations to real life: Parents can help students understand different types of equations in math by connecting them to everyday situations, like calculating shopping bills or dividing items.
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Use visual tools: Teachers can make abstract concepts clearer by using diagrams, number lines, or other visual aids to explain what an equation is in math.
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Promote step-by-step solving: Teachers should guide students to carefully manage parts of equations, moving variables and constants systematically to maintain balance and accuracy.
Common Mistakes and How to Avoid Them in Equations
Students can make mistakes while solving equations, resulting in wrong answers. The mistakes can happen in any equation, such as linear, quadratic, cubic, or rational. Given below are some mistakes that can happen while solving equations. To overcome these, solutions have been provided.
Mistake 1
Incorrect grouping of terms
Always group constants and like terms with the same variables. Children might mistakenly add the terms with variables directly to the constants, leading to incorrect results.
Mistake 2
Skipping steps while solving the equation
Mistake 3
Forgetting to check if the equation is solved correctly using the final result
To verify your solution, substitute the value of the variable into the equation and check if LHS equals RHS.
Mistake 4
Ignoring the ± sign while solving quadratic equations
While solving any quadratic equation, you need to remember that the square root of a variable will always be ±.
Mistake 5
Forgetting to change the sign of the constant.
Children often forget to change the sign of the constant when moved to another side.
Real-Life Applications of Equations
Equations are not just used to solve mathematical problems. They are used to solving practical problems as well. Some real-life applications are:
- Budget and Finance: Equations can track your expenditure and tell you how much you can save in a month.
- Time and Speed: To calculate the time to reach the destination or the speed required to get there, use the formula \(Speed = \frac{Distance}{Time}\)
- Electricity Usage: Used to calculate the electricity consumption of any device using the formula: \(Energy (in kWh) = Power (in kW) × Time (in hours)\)
- Cooking and Recipes: Equations help adjust ingredient quantities when changing the number of servings in a recipe. For example, if a recipe for 4 people uses 2 cups of flour, an equation helps calculate how much flour is needed for 6 people.
- Construction and Design: Builders use equations to calculate the amount of materials required, such as cement or tiles, ensuring accurate measurements and cost estimates for projects.
Solved Examples of Equations
Problem 1
Solve 3(x + 4) - 6 = 18.
4
Explanation
First, expand the bracket \(3(x + 4)\) → \(3x + 12\)
After the expansion, the equation will be \(3x + 12 - 6 = 18\)
Solving the equation, we get:
\(3x + 12 - 6 = 18\)
\(3x + 6 = 18\)
\(3x = 18 - 6\)
\(3x = 12\)
\(x = \frac{12}{3} = 4\)
Therefore, the value of x is 4
Problem 2
Solve 6y + 8 = 3y
The value of y is 2.
Explanation
The 3y on the RHS should be moved to the LHS, and -8 must be moved to the RHS. By doing so, we can group the terms with y on the LHS and the constants on the RHS.
Now the equation will look like this:\( 6y - 3y = -2 + 8\).
Solving for y we get:
\(6y - 3y = -2 + 8\)
\(3y = 6 ⇒ y = 2\)
Therefore, the value of y is 2
Problem 3
Solve x² + 6 = 31.
The result is ±5.
Explanation
\(x^2 + 6 = 31\)
\(x^2 = 31 - 6\)
\(x^2 = 25\)
\(x = \sqrt{25} = \pm 5 \)
Problem 4
Find the value of y in the equation (y + 3) / 2 = (y - 1) / 4.
The value of y is -7.
Explanation
Given equation: \(\frac{y + 3}{2} = \frac{y - 1}{4} \)
To remove the fraction, we can multiply the equation by the LCM of 2 and 4.
LCM of 2 and 4 = 4
Multiplying both side by 4:
\(4 \times \left( \frac{y + 3}{2} \right) = 4 \times \left( \frac{y - 1}{4} \right) \)
⇒ \(2y + 6 = y - 1\)
⇒ \(2y - y = (-1) + (-6)\)
⇒ \(y = -7\)
Problem 5
If x is given as 7, substitute 7 in the equation 5 (x - 2) = 3x + 4 and check if the LHS and RHS are the same.
Yes, the LHS and RHS are the same. Both LHS and RHS equal 25.
Explanation
By solving the LHS and RHS separately, we can determine if they have the same value.
\(5 (x - 2) = 5 (7 - 2) = 5 × 5 = 25\)
The LHS is 25
\(3x + 4 = (3 × 7) + 4 = 21 + 4 = 25\)
The RHS is 25
Therefore, LHS = RHS
FAQs on Equations
1.Write the types of equations based on their degree.
2.How to solve an equation?
3.What do you mean by differential equations?
4.What is the main difference between an expression and an equation?
5.What is the general form of a quadratic equation?
6.How can I help my child practice equations at home?
7.What are some common challenges students face while learning equations?
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.
