INVERSE PROPERTY OF ADDITION

Words : 

The sum of a real number and its opposite (additive inverse) is zero. 

Numbers : 

3 + (-3)  =  (-3) + 3  =  0

Algebra : 

For any real number a, 

a + (-a) + (-a) + a  =  0

Note : 

(i) If a number is positive, then its opposite or additive inverse is the same number with negative sign.

(ii) If a number is negative, then its opposite or additive inverse is the same number with positive sign.  

Examples : 

2 and -2 are opposites

3 and -3 are opposites

Problem 1 :

If x and y are additive inverse to each other, find x in terms of y. 

Solution :

Because x and y are additive inverse to each other, their sum is zero. 

x + y  =  0

Solve for x : Subtract y from each side. 

x  =  -y

Problem 2 : 

If 3y and 9 are additive inverse to each other, find the value of y. 

Solution :

Because 3y and 9 are additive inverse to each other, their sum is zero.  

3y + 9  =  0

Subtract 9 from each side.  

3y  =  -9

Divide each side by 3. 

y  =  -3

Problem 3 : 

For what value of x, (2 + 5x) and 3 are additive inverse to each other ? 

Solution :

If (2 + 5x) and 3 are additive inverse to each other, their sum is zero. 

(2 + 5x) + 3  =  0

2 + 5x + 3  =  0

5x + 5  =  0

Subtract 5 from each side. 

5x  =  -5

Divide each side by 5. 

x  =  -1

Problem 4 : 

Are (7 - k) and k additive inverse to each other ?, if so, find the value of k. 

Solution :

To verify whether (7 - k) and k are additive inverse to each other, add them

(7 - k) + k  =  7 - k + k

=  7

Because the sum is not zero, (7 - k) and k are not additive inverse to each other. 

Problem 5 : 

If p - q  = 24, p and q are additive inverses, find the value of p. 

Solution :

Given :

p - q  =  24 -----(1)

Because p and q are additive inverse to each other, their sum is zero. 

p + q  =  0 -----(2)

(1) + (2) : 

2p  =  24

Divide each side by 2. 

p  =  12

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