Equation

Equations show how LHS and RHS are related. We use them to find unknown variables. Without an = sign, we cannot write an equation.

For example, a = 10b - 5 is an equation, whereas p³+q - 6 is not an equation.

Even though we use both expressions and equations in algebra, they are different from each other. The table below illustrates the differences between them.
 

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 students 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

Linear equations are those equations where the highest degree of variables is 1. They can be classified based on the number of variables. E.g., equations with only one variable are called one-variable linear equations, and so on. The general form of a linear equation can be represented as:

aP + bQ + c = 0, where a and b are the coefficients of the variables P and Q, while c is the constant. Here, the highest degree of variables P and Q is 1.

In quadratic equations, the highest degree of the variable will always be 2. The general form of a quadratic equation with m as the variable will be:

am² + bm + c = 0 where a ≠ 0. 

In the equation: 

• m² is the variable with 2 as the highest degree, and a is the coefficient of m². If a is zero, then the equation cannot be quadratic.
   
• c is the constant.

In cubic equations, one of the variables will have 3 as the highest degree. The general form of a cubic equation will be:

ax³ + bx² + cx + d = 0, where x³ is the variable with the highest degree. a, b, and c are coefficients of x³, x², and x respectively, and d is the constant.

Equations containing a fraction, where the numerator or denominator or both contain a variable, are rational equations. The rational equation is: 

b/3 = a+c/4

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:

3x + 15 = 24

Here, the 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

An equation means LHS should be equal to RHS. Any changes made on the LHS should be done on the RHS too. To find an unknown variable, we must solve the equation while maintaining the balance on both LHS and RHS. 

Let's see how to solve a basic equation, 3x - 2 = 4. Follow the steps given below:

Step 1: Make the terms with variables to be on one side and the constants on the other side. Here, 3x will remain on the LHS, and 2 will go to the RHS. Since the constant -2 is going to the RHS, it will become +2.

Step 2: Now the equation will be 3x = 4 + 2

Step 3: Add the values on the RHS. The equation will be 3x = 6

Step 4: To find the value of x, we need to shift 3 to the RHS. Since 3 and x are connected by multiplication on the LHS, shifting 3 to the RHS will change its sign from multiplication to division. So, dividing 6 by 3, we get the value of x as 2
→ 3x = 6 → x = 6/3 = 2

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 = 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)