Introduction: - Expression: - x + 2 Equation: - x + 2 = 20 x2 + 2x + 5 = 12 Linear Equation: - x + 2 = 20 => x1 + 2 =20 y2+ 5 = 2y + 6 => y2 + 5 = 2y1 + 6 Solving Equation 1) Variable on one side Method 1 : - e.g. 2x – 3 = 5 2x -3 + 3 = 5 + 3 (add 3 on both sides) 2x = 8 𝟐𝒙/𝟐= 𝟖/𝟐 x = 4 Method 2: - Transpose e.g. 2x – 3 = 5 2 x = 5 + 3 2 x = 8 X = 𝟖/𝟐 X = 4 2) Variable on both sides e.g. 3x – 4 = x + 2 Verify 3x – x = 2 + 4 LHS = 3x -4 2x = 6 3*3 – 4 = 5 x = 𝟔/𝟐 RHS = x + 2 x = 3 3 + 2 = 5   So, LHS = RHS Solving Word Problems: - Que) A man is 25 years older than his son. After 5 years, he will be two times as old as his son. Find their present ages. Solution: - Let’s sons present age = x years Then father’s age = x + 25 After 5 years, Son’s age = x + 5 Father’s age = (x + 25) + 5 = x + 30 Given, x + 30 = 2*(x + 5) x + 30 = 2x + 10 x – 2x = 10 – 30 -x = -20 x = 20 = son’s age Fathers age = 20 + 25 = 45 years.

1. Mayur. U. Rahangdale
BE, M.Tech

2. Introduction: -
Expression: -
x + 2
Equation: -
x + 2 = 20
x2 + 2x + 5 = 12
Linear Equation: -
x + 2 = 20 => x1 + 2 =20
y2+ 5 = 2y + 6 => y2 + 5 = 2y1 + 6

3. Solving Equation
1) Variable on one side
Method 1 : -
e.g. 2x – 3 = 5
2x -3 + 3 = 5 + 3 (add 3 on both sides)
2x = 8
𝟐𝒙
𝟐
=
𝟖
𝟐
x = 4

4. Method 2: - Transpose
e.g. 2x – 3 = 5
2 x = 5 + 3
2 x = 8
X =
𝟖
𝟐
X = 4

5. 2) Variable on both sides
e.g. 3x – 4 = x + 2 Verify
3x – x = 2 + 4 LHS = 3x -4
2x = 6 3*3 – 4 = 5
x =
𝟔
𝟐
RHS = x + 2
x = 3 3 + 2 = 5
So, LHS = RHS

6. Solving Word Problems: -
Que) A man is 25 years older than his son. After 5 years, he will be two times as old as his
son. Find their present ages.
Solution: -
Let’s sons present age = x years
Then father’s age = x + 25
After 5 years,
Son’s age = x + 5
Father’s age = (x + 25) + 5 = x + 30
Given, x + 30 = 2*(x + 5)
x + 30 = 2x + 10
x – 2x = 10 – 30
-x = -20
x = 20 = son’s age
Fathers age = 20 + 25 = 45 years.