Since, b - 2 = 1
⇒ b = 1 + 2
⇒ b = 3

For any integer a, we have (- 1) x a = - a

We have, 18 x [ 7+ (- 3) ] = [ 18 x 7 ] + [ 18 x (- 3) ]
\(\therefore\) LHS = 18 x [ 7+ (-3) ] = 18 x (7-3) = 18 x 4 = 72
and RHS = [ 18 x 7] + [18 x (- 3) ] = 126 + [ (- 54) ]
= 126 - 54 = 72
\(\because\) LHS = RHS
Hence, 18 x  [ 7 + (- 3) ] = [18 x 7] + [ 18 x (- 3) ]

We have, (-15) x 0 x (-18) = [ (-15) x 0 ] x (-18)
= 0 x (-18) = 0

We have, (-31) x (-100) = 31 x 100 =3100

We have, 7 x (- 22) = - (7 x 22)= -154

We have, 12 x (- 32) = - (12 x 32) = - 384

-12 and 6

A pair of integers, whose sum is - 7, can be - 2 and - 5.
\(\because\)  Sum = -2 + (-5) = -2 -5 = -7

-23 + 32 and 32 + (-23)
For addition -23 + 32 = +9     [\(\because\)(-)( +) = (-) and higher integer sign is (+)]
Verification First integer (x) = - 23
Second integer (y) = 32
Forcommutativeproperty: x+y=-23+32=9 and y+x=32+(-23)=32-23=9 \(\Rightarrow\) x+ y=y+x
i.e. commutative property is closed for addition.

Preceding integers = -10, -9, -8
Succeeding integers = -6, -5, -4

Given, a = 75 and b = 84
\(\therefore\) LHS = a - (-b) = 75 - (-84) = 75 + 84 =159
and RHS = a + b = 75 + 84 = 159
Hence, LHS = RHS

Correct, when a number and its opposite add up to give zero, they are called additive inverse of each other. In other words, the additive inverse of a number is the opposite of that number.
e.g.

(-6) - (-16) = -6 + (16)= + 10 or 10    [\(\because\) (-)( -) = (+), difference = 10, higher integer sign is '+']

14-(-20)=14+(20)=34          [\(\because\) (-)(-) = +]