Algebraic Expression

1. Algebraic Equation
Grade-6
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
9a1 + 6 =0
3x1 +1= 7
3a4+1=2
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. Conversion of a statement to an Equation
• 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.