Exercise 8.2
Solve each of the following equation and check your answer:
1. x – 3 = 5
Solution:
Given x – 3 = 5
Adding 3 to both sides, we get
x – 3 + 3 = 5 + 3
x = 8
Verification:
Substituting x = 8 in LHS, we get
LHS = x – 3 and RHS = 5
LHS = 8 – 3 = 5 and RHS = 5
LHS = RHS
Thus, verified.
2. x + 9 = 13
Solution:
x + 9 = 13
Subtracting 9 from both sides, we get
=> x + 9 – 9 = 13 – 9
=> x = 4
Verification:
Substituting x = 4 on LHS, we get
LHS = 4 + 9 = 13 = RHS
LHS = RHS
Thus, verified.
4. 3x = 0
Solution:
3x = 0
Dividing both sides by 3, we get
3x/3 = 0/3
x = 0
Verification:
Substituting x = 0 in LHS = 3x, we get LHS = 3 × 0 = 0 and RHS = 0
LHS = RHS
Thus, verified.
5. x/2 = 0
Solution:
x/2 = 0
Multiplying both sides by 2, we get
=> (x/2) × 2 = 0 × 2
=> x = 0
Verification:
Substituting x = 0 in LHS, we get
LHS = 0/2 = 0 and RHS = 0
LHS = 0 and RHS = 0
LHS = RHS
6. x – (1/3) = (2/3)
Solution:
Given x – (1/3) = (2/3)
Adding (1/3) to both sides, we get
X – (1/3) + (1/3) = (2/3) + (1/3)
X = (1/3) + (1/3) = (2/3) + (1/3)
X = (3/3)
X = 1
Verification:
Substituting x = in LHS, WE GET
1 – (1/3) = (2/3)
2/3) = (2/3)
Therefore LHS = RHS
Thus, verified.
8. 10 – y = 6
Solution:
Given: 10 – y = 6
Subtracting 10 from both sides, we get
10 – y – 10 = 6 – 10
-y = -4
Multiplying both sides by -1, we get
-y × -1 = – 4 × – 1
y = 4
Verification:
Substituting y = 4 in LHS, we get
LHS = 10 – y = 10 – 4 = 6 and RHS = 6
LHS = RHS
Thus, verified.
9. 7 + 4y = – 5
Solution:
Given: 7 + 4y = -5
Subtracting 7 from both sides, we get
7 + 4y – 7 = -5 -7
4y = -12
Dividing both sides by 4, we get
y = -12/ 4
y = -3
Verification:
Substituting y = -3 in LHS, we get
LHS = 7 + 4y = 7 + 4(-3) = 7 – 12 = -5, and RHS = -5
LHS = RHS
Thus, verified.
10. (4/5) – x = (3/5)
Solution:
Given (4/5) – x = (3/5)
Subtracted (4/5) – x (3/5) – (4/5)
– x = (3-4)/5
– x = (-1/5)
X = (1/5)
Verification:
Substituting x = (1/5) in LHS we get
(4/5) – (1/5) = (3/5)
(4-1)/ 5 (3/5)
(3/5) = (3/5)
Therefore LHS = RHS
Thus, verified.
12. 14 + (7x-/10) – 8
Solution:
Given 14 = (7x/10) – 8
Adding 8 to both sides we get,
14 + 8 = (x/10)
Multiplying both sides by 10 we get,
220 = 7x
X =(220/7)
X = (220/7)
Verification:
Substituting x = (220/7) in RHS we get,
14 = (7/10) (220/7) – 8
14 = 22-8
14 = 14
Therefore LHS = RHS
Thus, verified.
13. 3(x + 2) = 15
Solution:
3 (x + 2) = 15
Dividing both sides by 3, we get
14. x/4 = 7/8
Solution:
x/4 = 7/8
Multiplying both sides by 4, we get
15. 1/3 – 2x = 0
Solution:
1/3 – 2x = 0
Subtracting 13 from both sides, we get
16. 3 (x+6) = 24
Solution:
3 (x+6) = 24
=> 3x + 18 = 24
=> 3x+ = 24 – 18
=> 3x = 6
=> x = 1/6
=> x = 2
17. 3(x + 2) – 2(x – 1) = 7
Solution:
3(x + 2) – 2(x – 1) = 7
On expanding the brackets, we get
3× x + 3 × 2 – 2 × x + 2 × 1 = 7
3x + 6 – 2x + 2 = 7
3x – 2x + 6 + 2 = 7
x + 8 = 7
Subtracting 8 from both sides, we get
x + 8 – 8 = 7 – 8
x = -1
Verification:
Substituting x = -1 in LHS, we get
LHS = 3 (x + 2) -2(x -1) = 3 (-1 + 2) -2(-1-1) = (3×1) – (2×-2) = 3 + 4 = 7, and RHS = 7
LHS = RHS
Thus, verified.
18. 8(2x – 5) – 6(3x – 7) = 1
Solution:
8(2x – 5) – 6(3x – 7) = 1
On expanding the brackets, we get (8 × 2x) – (8 × 5) – (6 × 3x) + (-6) × (-7) = 1
16x – 40 – 18x + 42 = 1
16x – 18x + 42 – 40 = 1
-2x + 2 = 1
Subtracting 2 from both sides, we get
-2x+ 2 – 2 = 1 -2
-2x = -1
Multiplying both sides by -1, we get
-2x × (-1) = -1× (-1)
2x = 1
Dividing both sides by 2, we get
19. 6(1 – 4x) + 7(2 + 5x) = 53
Solution:
6(1 – 4x) + 7(2 + 5x) = 53
On expanding the brackets, we get (6 ×1) – (6 × 4x) + (7 × 2) + (7 × 5x) = 53
6 – 24x + 14 + 35x = 53
6 + 14 + 35x – 24x = 53
20 + 11x = 53
Subtracting 20 from both sides, we get 20 + 11x – 20 = 53 – 20
11x = 33
Dividing both sides by 11, we get
11x/11 = 33/11
x = 3
Verification:
Substituting x = 3 in LHS, we get
= 6(1 – 4 × 3) + 7(2 + 5 × 3)
= 6(1 – 12) + 7(2 + 15)
= 6(-11) + 7(17)
= – 66 + 119
= 53 = RHS
LHS = RHS
Thus, verified.
20. 5 (2-3x) – 117 (2x-5) = 16
Solution:
5 (2-3x) – 117 (2x-5) = 16
= 10 – 15x – 34x + 88 = 16
= 10 – 49x + 85 = 16
= 95 – 16 = 49x
= 95 – 16 = 49x
= 49x = 79
= x =79/49
21.( x -3) / 5-2 = -1
Solution:
Given ((x-3)/5)-2 = -1
Adding 2 to both sides we get
((x- 3)/5 – 2+ = -1 + 2
( x – 3) / 5 = 1
Multiplying both sides by 5 we get
(x-3) / 5×5 = 1×5
X – 3 = 5
Now add to both sides we get,
X – 3 + 3 = 5 + 3
X = 8
Verification:
Substituting x = 8 in LHS we get, ((8-3)/5- 2 = -1
(5/5) – 2 = -1
(5/5) – 2= -1
(5/5) – 2 = =1
1-2 = -1
Therefore LHS = RHS
Thus, verified.
2. 5(x – 2) +3(x + 1) = 25
Solution:
5(x – 2) + 3(x + 1) = 25
On expanding the brackets, we get
(5 × x) – (5 × 2) +3× x + 3× 1 = 25
5x – 10 + 3x + 3 = 25
5x + 3x – 10 + 3 = 25
8x – 7 = 25
Adding 7 to both sides, we get
8x – 7 + 7 = 25 + 7
8x = 32
Dividing both sides by 8, we get
8x/8 = 32/8
x = 4
Verification :
Substituting x = 4 in LHS, we get
= 5(4 – 2) + 3(4 + 1) = 5(2) + 3(5) = 10 + 15 = 25 = RHS
LHS = RHS
Thus, verified.