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Notes:

Equation: Any mathematical expression equating one algebraic expression to another is called as an equation.

Some examples of equations are 6x = 36, 2x – 3 = 18, x2 -- 1 = 0, etc.

Linear Equation:

1. An equation of the form ax + b = 0 where a, b are real numbers such that ‘a’ should not be equal to zero is called a linear equation.

2. Remember, the highest power of the variable in these expressions is 1.

3. Examples of some linear equations are 6x, 3x+5, 10 – 5p, etc.

4. Examples of some non-linear equations are x2 + 1, y + y2, etc. In these examples, the power of variable is greater than 1, thus they are non-linear equations.

Some key points:

(i) For any linear equation, there will be a presence of an equal to sign in the equation.

(ii) The quantity on left of the equality sign is called the Left Hand Side (LHS) of the equation and that on the right side is called the Right Hand Side (RHS) of equation. The values of the expression on the LHS and RHS are equal and become true only for certain values of the variable. These certain values are called the solutions of the equation.

(iii) Every linear equation has ONE unique solution.

Solving Linear Equations:

In this method, both the sides of equation are balanced. Let us understand it by an example:

Example: Solve 2n -- 10 = 2.

Solution: To balance both the sides, firstly we will add 10 on both the sides of the equation.

• 2n – 10 + 10 = 2 +10,

On solving, we get

• 2n = 12

Further, to balance the equation we will divide both the sides by 2

• 2n / 2 = 12/2

On solving, we get

• n = 6.
• Thus, n = 6 is the required solution.

(2) Transposing Method:

In this method, constants or variables are transposed from one side of the equation to other until the solution is obtained. Let us understand it by an example:

Example: Solve 2x – 15 = 5

Solution: Firstly, we will transpose the integer -5 from LHS to RHS, thus we will get

2x = 5 + 15

On solving, we get

Now, we will transpose the 2 from LHS to RHS, thus we will get

x = 20 / 2

On solving, we get

x = 10.

Thus, x = 10 is the required solution.

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