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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