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In which of the following cases does an equality NOT hold?
- a)Adding the same number on both the sides.
- b)Not performing the same operation on both the sides.
- c)Subtracting the same number from both the sides.
- d)Multiplying both the sides by the same non-zero number.
Correct answer is option 'B'. Can you explain this answer?
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In which of the following cases does an equality NOT hold?a)Adding the...
Explanation:
In this question, we are given four cases and we have to determine in which case an equality does not hold. Let's analyze each case to understand why an equality does not hold in each case.
a) Adding the same number on both sides:
When we add the same number on both sides of an equation, the equality holds. This is because we are maintaining the balance by performing the same operation on both sides. For example:
2 + 3 = 5
Adding 4 on both sides:
2 + 3 + 4 = 5 + 4
9 = 9
The equality holds.
b) Not performing the same operation on both sides:
When we do not perform the same operation on both sides of an equation, the equality does not hold. This is because we are not maintaining the balance by performing different operations on both sides. For example:
2 + 3 = 5
Adding 4 on one side only:
2 + 3 + 4 ≠ 5 + 4
9 + 4 ≠ 9
13 ≠ 9
The equality does not hold.
c) Subtracting the same number from both sides:
When we subtract the same number from both sides of an equation, the equality holds. This is because we are maintaining the balance by performing the same operation on both sides. For example:
2 + 3 = 5
Subtracting 3 from both sides:
2 + 3 - 3 = 5 - 3
2 = 2
The equality holds.
d) Multiplying both sides by the same non-zero number:
When we multiply both sides of an equation by the same non-zero number, the equality holds. This is because we are maintaining the balance by performing the same operation on both sides. For example:
2 + 3 = 5
Multiplying both sides by 2:
2(2 + 3) = 2(5)
4 + 6 = 10
10 = 10
The equality holds.
Conclusion:
From the analysis above, we can see that the only case where an equality does not hold is when we do not perform the same operation on both sides of an equation. In all other cases (adding the same number, subtracting the same number, multiplying both sides by the same non-zero number), the equality holds because we are maintaining the balance by performing the same operation on both sides.
In this question, we are given four cases and we have to determine in which case an equality does not hold. Let's analyze each case to understand why an equality does not hold in each case.
a) Adding the same number on both sides:
When we add the same number on both sides of an equation, the equality holds. This is because we are maintaining the balance by performing the same operation on both sides. For example:
2 + 3 = 5
Adding 4 on both sides:
2 + 3 + 4 = 5 + 4
9 = 9
The equality holds.
b) Not performing the same operation on both sides:
When we do not perform the same operation on both sides of an equation, the equality does not hold. This is because we are not maintaining the balance by performing different operations on both sides. For example:
2 + 3 = 5
Adding 4 on one side only:
2 + 3 + 4 ≠ 5 + 4
9 + 4 ≠ 9
13 ≠ 9
The equality does not hold.
c) Subtracting the same number from both sides:
When we subtract the same number from both sides of an equation, the equality holds. This is because we are maintaining the balance by performing the same operation on both sides. For example:
2 + 3 = 5
Subtracting 3 from both sides:
2 + 3 - 3 = 5 - 3
2 = 2
The equality holds.
d) Multiplying both sides by the same non-zero number:
When we multiply both sides of an equation by the same non-zero number, the equality holds. This is because we are maintaining the balance by performing the same operation on both sides. For example:
2 + 3 = 5
Multiplying both sides by 2:
2(2 + 3) = 2(5)
4 + 6 = 10
10 = 10
The equality holds.
Conclusion:
From the analysis above, we can see that the only case where an equality does not hold is when we do not perform the same operation on both sides of an equation. In all other cases (adding the same number, subtracting the same number, multiplying both sides by the same non-zero number), the equality holds because we are maintaining the balance by performing the same operation on both sides.
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