This document provides examples of linear equations in one variable and methods for solving them. It defines linear equations as those with a maximum power of 1 and provides examples. Methods for solving linear equations are presented, including balancing, transposition, and substitution. Practical word problems involving linear equations are also worked through with solutions.

1. Linear Equation in One Variable
Grade-7
Shepherd’s Path International
Academy

2. Equation
• The statement of equality containing a variable is called equation
3x+6 = 0
4x +4 =8
7v + 9 = 9

3. Linear Equation
• Linear equation is an equation in which maximum power of a variable
is 1 .
3x +5 =1
9a + 6 =0
But 8x2 + 7 = 6 is not a linear equation because its power is not 1.

4. Linear equation n one variable
• An equation that involves only one variable.
4x - 8 =5
2a + 5 =0

5. Conversion of a statement to an equation
• The sum of 5 times of x and 7 times of y is 60
• A number is exceeds 6 by 4.

6. • The number is 5 more than 12
• One third of a number a is 6 more than 5.

7. Conversion of an equation to a statement
• 5a + 6= 21
• 2x +y = 4

8. •
𝑦
2
+ 4=9

9. Checking the solution of an equation
• 𝑥 + 5 = 12 𝑥 = 7
• 𝑦 + 8 = 14 𝑦 = 4
• 3𝑎 + 7 = 16 𝑎 = 3

10. Solving Equation
• Method of Balancing
• 𝑥 − 2 = 10
Adding 2 both side
• 𝑥 − 2 + 2 = 10 + 2
• 𝑥 = 12

11. 𝑦
3
= 6
•
𝑦
3
= 6
Multiply both side by 3
𝑦
3
𝑥3 = 6 𝑥3
𝑦 = 18

12. Method of transposition
• + becomes – on changing the side
• - becomes positive on changing side
• x becomes ÷ on changing the side
• ÷ becomes x on changing the side

13. 2x+8=60
• 2x +8 =60
• 2x = 60-8
• 2x= 52
• x=
52
2
• x = 26

14. 𝑦
3
− 2 = 5
•
𝑦
3
− 2 = 5
•
𝑦
3
= 5 + 2
•
𝑦
3
= 7
• 𝑦 = 7 × 3
• 𝑦 = 21

15. Find the value of x
• 4x + 8 = 32
• 7x+3=45
• 9x-2=61

16. Solve the linear equation by method of
balancing
• 2(a+5) = 2
•
3𝑞
4
- 1 = 5

17. Solve the linear equation and then verify the
solution
• 3(p+2) +4 = 10
• 9(a+2) =108

18. Solve the following linear equation
• 15 𝑥 − 4 − 2 𝑥 + 3 − 3 𝑥 + 8 = 0
Solution: 15 𝑥 − 4 − 2 𝑥 + 3 − 3 𝑥 + 8 = 0
15𝑥 − 60 − 2𝑥 − 6 − 3𝑥 − 24 =0
10𝑥 − 90 = 0
10𝑥 = 90
𝑥 =
90
10
= 9
𝑥 = 9

19. solve
• 2.7𝑥 − 1.9 − 0.2𝑥 = 0.1(3 − 𝑥)

20. 5𝑥 − 1
2
−
5𝑥 − 2
3
= 1
• Solution:
5𝑥−1
2
−
5𝑥−2
3
= 1
multiplying both side of the equation by 6 , the lcm of 2 and 3 , we get
6
5𝑥−1
2
− 6 ×
5𝑥−2
3
= 1 × 6
3 5𝑥 − 1 − 2 5𝑥 − 2 = 6
15𝑥 − 3 − 10𝑥 + 4 = 6
5𝑥 + 1 = 6
5𝑥 = 6 − 1
5𝑥 = 5
𝑥 =
5
5
= 1

21. solve
•
14𝑥+20
10𝑥+20
=
9
7

22. Solve
2
3
𝑥 − 5 −
1
4
−𝑥 − 2 =
9
2

23. Practical application
• The length of a rectangle is 6m less than three times its breadth. Find the dimensions of the rectangle it its
perimeter is 148m.
solution : let us assume the breadth of the rectangle to be 𝑥
the length of rectangle = 3𝑥 − 6
the perimeter of a rectangle = 148m
2( length + breadth ) = 148
2 (3𝑥 − 6 + 𝑥) = 148
2(4𝑥 − 6) = 148
(4𝑥 − 6) =
148
2
4𝑥 − 6 = 74
4𝑥 = 74 + 6
4𝑥 = 80
𝑥 =
80
4
= 20

24. Divide 80 into equal parts such that the
greatest part is four times the smaller part.
• Solution: let the smaller part be x .
the greater part =4x
According to question, smaller part + greater part=80
𝑥 + 4𝑥 = 80
5𝑥 = 80
𝑥 =
80
5
𝑥 = 16
Smaller part = 16 , Greater part = 16 x 4 = 64

25. In a class of 35 students, the number of girls is two
fifth the number of boys . Find the number of boys
in the class.

26. • Three forth of a number is greater than two third of a number by 7.
find the number.

27. • The sum of two consecutive integers is 49. Find the number?

28. • One number is 4 less than times another number, if a sum is
increased by 5 ,the result is 25. find both the number.