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**Question 1: Find the additive inverse of each of the following integers:(i) 52(ii) âˆ’176(iii) 0(iv) 1ANSWER: **THE ADDITIVE INVERSE OF THE NUMBER A IS THE NUMBER ADDED TO A, YIELDS ZERO. SO, WE FIND THE FOLLOWING:

(i) 52 + (âˆ’52) = 0Here, âˆ’52 is the additive inverse of 52.

(ii) (âˆ’176) + 176 = 0Here, 176 is the additive inverse of âˆ’176.

(iii) 0 + 0 = 0Here, 0 itself is its inverse.

(iv) 1 + (âˆ’1) = 0Here, âˆ’1 is the additive inverse of 1.

Question 2:

Find the successor of each of the following integers:**(i) âˆ’42(ii) âˆ’1(iii) 0(iv) âˆ’200(v) âˆ’99**

(i) âˆ’41 is the successor of âˆ’42.

(ii) 0 is the successor of âˆ’1.

(iii) 1 is the successor of 0.

(iv) âˆ’199 is the successor of 200.

(v) âˆ’98 is the successor of âˆ’99.

**Find the predecessor of each of the following integers:(i) 0(ii) 1(iii) âˆ’1(iv) âˆ’125(v) 1000**

For the integer a, the predecessor is (a âˆ’ 1).

(i) âˆ’1 is the predecessor of 0.

(ii) 0 is the predecessor of 1.

(iii) âˆ’2 is the predecessor of âˆ’1.

(iv) âˆ’126 is the predecessor of âˆ’125.

(v) 999 is the predecessor of 1000

**Which of the following statements are true?(i) The sum of a number and its opposite zero.(ii) The sum of two negative integer is positive integer.(iii) The sum of a negative integer and a positive integer is always a negative integer.(iv) The successor of âˆ’1 is 1.(v) The sum of three different integers can never be zero.**

(i) True âˆ’ It is the definition of additive inverse; for example, 5 + (âˆ’5) = 0.

(ii) False âˆ’ For example, âˆ’2 âˆ’ 3 = âˆ’5; it is a negative integer.

(iii) False âˆ’ âˆ’3 + 5 = 2; it is a positive integer.

(iv) False âˆ’ 0 is the successor of âˆ’1.

(v) False âˆ’ It can be zero like (âˆ’2) + (âˆ’1) + (3).

Question 5:

ANSWER:

âˆ´ -5 < x < 5

=> x = ] -4, 4 [

These are the nine integers whose absolute values are less than 5, namely, -4, -3, -2, -1, 0, 1, 2, 3 and 4.

Which of the following is false:

(i)|4+2|=|4|+|2|

(ii) |2-4|=|2|+|4|

(iii

(i) |4|+ |2| = 6 = |4| + |2|; True

(ii) |2 âˆ’ 4| = |âˆ’2| = 2 â‰ 2 + 4 = 6; False

(iii) |4 âˆ’ 2| = 2 = |4| âˆ’ |2|; True

(iv) |(âˆ’2) + (âˆ’4)| = |âˆ’6| = 6 = |âˆ’2| + |(âˆ’4)|; True