The document discusses methods for solving linear equations, detailing two approaches: isolating variables and transposing. It also includes a word problem involving the ages of a father and son, demonstrating how to set up and solve the equation to find their current ages. The solution reveals the son is 20 years old and the father is 45 years old.

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.