What is an Equation

Definition:

An equation is a mathematical statement with an ‘equality’ sign between two algebraic expression. The equality sign shows that the value of the expression to the left of the side (LHS or left hand side) is equal to the value of the expression to the right hand side (RHS or right hand side). Highest power of a linear equation is 1.

Example: In equation 3x + 5 = 20

The left hand side (LHS) is (3x + 5).

The right hand side is 20.

In equation 4x – 3 = 5

The left hand side (LHS) is (4x – 3) and the right hand side (RHS) is 5.

We apply mathematical operations on the LHS and the RHS, and we note that the balance is not disturbed.

If we add or subtract the same number from both sides of an equation, equation remains same.

Let’ an equation 2x – 3 = 5

Let’s add 3 on both sides to reduce the LHS to 2x and RHS is gain 3. This will not disturb the balance.

The new LHS is 2x – 3 + 3 = 2x, and new RHS is 5 + 3 = 8

Similarly, if we multiply or divide the same number on both sides of equation, equation remains same.

Now we divide both sides by 2, LHS is 2x/2 equal to x and RHS will be 4/2 equal to 2.

Thus the solution of the equation is x = 4. This will not disturb the balance.

x² +5, y³ – 4, p² + p³, These are not linear equations because highest power of variable is > then 1.

If there is not a equality sign but some other sign than equality sign between the LHS and RHS, then it is not an equation.

Example: 3x + 5 > 20 is not an equation. It means the value of (3x + 5) is greater than 20.

Similarly, 3x + 5 < 20, means is not an equation. It means the value of (3x + 5) is smaller than 20.

The equation 4x – 9 = 11 is same as 11 = 4x – 9.

Similarly, the equation 5x + 3 = 2x + 15 is same as 2x + 15 = 5x +3.

When the expression on the left and on the right are interchanged, equation remains the same. This property is very useful for solving equations.

We notice that, in equations the RHS is just a number, but this need not be always so.

The RHS of an equation may be an expression containing the variable, example: 25 = 5x + 10

There are 3 main types of equations.

Linear Equation
Quadratic Equation
Cubic Equation