The document discusses linear equations in one variable, providing definitions, examples of solving equations, and applications through word problems. It includes step-by-step solutions for various equations and scenarios, emphasizing the method of transposing terms. Notably, it illustrates how to set up and solve real-life problems involving age and numerical relations.

2. 1. Meaning of the Chapter’
2. Solution of an Equation.
3. Word problems.
( Applications of linear equation in one
variable.)

3. Terms
Constants & Variables
Algebraic Expression
Equation

4. EQUATION
A statement which states that two algebraic expressions
are equal is called an equation.
3x-2y=8
6-x = x+9
LINEAR EQUATION IN ONE VARIABLE
The equation involving only one variable in first order is called a
linear equation in one variable
3x-5=0
8-y=2

5. Linear Equation in one variable.
Equation
2x -3 =7
Variables Equality

6. Solve an Equation
1.To solve an equation of the form x+a=b
2. To solve an equation of form x-a=b

7. Transpose the terms containing the variables to one side
and constants to the other side
EXAMPLE 1 Solve 10y-3=7y+9
SOL: 10y-7y=9+3 (transposing 7y to left & 3 to the right)
=> 3y=12
=> y=12/3
=> y = 4
EXAMPLE 2 Solve 2(x-5) + 3(x-2) = 8+7(x-4)
SOL: 2x-10+3x-6 = 8=7x-28 (removing the brackets)
=> 5x-16 = 7x-20
=> 5x-7x = -20+16
=> -2x = -4
=> x = -4/-2
=> x = 2

8. SOLVING WORD PROBLEMS
• QUES : A number increased by 8 equal 15. Find the
number ?
Solution: Let the number be 'x'
=> x+8 = 15
=> x = 15-8
=> x = 7

9. QUES: A number is decreased by 15 and the new number so obtained is
multiplied by 3; the result is 81. Find the number ?
SOLUTION: Let the number be 'x'
The number decreased by 15 = x-
15
The new number (x-15) multiplied
by 3 = 3(x-15)
Given 3(x-15) = 81
=> 3x-45=81
=> 3x=81+45
=> x=126/3
=> x=42

10. QUES: A man is 26 years older than his son. After 10 years, he
will be three times as old as his son. Find their present ages.
SOL: Let son's present age= x years
Then father's age = x+26 years
After ten years,
Son's age = x+10
Father's age = x+26+10 = x+36
Given, x+36=3(x+10)
=> x+36 = 3x+30
=> x-3x = 30-36
=> -2x = -6
=> x = -6/-2
=> x = 3
•Son's age = 3 years
•Father's age = 3 + 26 = 29 years