Question

9 Simplify:
{-17 + (-21)} + { -29 - (-23)}
10 The sum of two integers is -27. If one of them is -71, find the other.

11 The difference of an integer a and -77 is -125, find the value of a.

12 The difference of -13 and a is -19, find the value of a.

13 If a = -13 and b = -12, show that a - b + b - a.

14 If a = -9, b = -7 and c = 11, verify that (a + b) + c = a +
(b+c)
​

Answer 1

Question : 9

$\sf \: Simplify \rightarrow$

$\bf\implies -17 + (-21) + (-29) - (-23)$

$\implies\sf -17 - 21 - 29 - (-23)$

$\implies\sf -17 - 21 - 29 + 23$

$\sf\implies - 38 - 29 + 23$

$\sf \implies - 67 + 23$

$\boxed{ \red{\bf\implies Answer = - 44}}$

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Question : 10

$\sf\implies Sum \: of \: two \: integers = - 27$

$\sf\implies One \: of \: them = - 71$

$\sf\implies Other \: integer = \: ?$

$\sf Equation = \bf-71+x = -27$

$\sf\implies x = - 27 - ( - 71)$

$\sf\implies x = - 27 + 71$

$\sf\implies x = 44$

$\boxed{ \red{\bf \: So, the \: other \: integer \: is \: 44}}$

________________________________

Question : 11

$\sf\implies a-(-77)= -125$

$\sf\implies Value \: of \: a = \: ?$

Now,

$\sf\implies a + 77= -125$

$\sf\implies a = - 125 - 77$

$\boxed{ \red{\bf\implies a = - 202}}$

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Question : 12

$\sf\implies - 13 - a = - 19$

$\sf\implies Value \: of \: a = \: ?$

Now,

$\sf\implies - a = - 19 + 13$

$\sf\implies - a = - 6$

$\boxed{ \red{\bf\implies a = 6}}$

________________________________

Question : 13

$\sf\implies a = - 13$

$\sf\implies b= - 12$

$\sf\implies Show \: that \: \underline{ a - b + b - a}$

Now,

$\sf\implies - 13 - ( - 12) + ( - 12) - ( - 13)$

$\sf\implies - 13 + 12 - 12 + 13$

$\sf\implies - 1 - 12 + 13$

$\sf\implies - 13 + 13$

$\boxed{ \red{\bf\implies Answer = 0}}$

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Question : 14

$\sf\implies a = - 9$

$\sf\implies b= - 7$

$\sf\implies c= 11$

$\sf\implies Verify \: that \: \underline{ (a+b)+c=a+(b+c)}$

Now,

$\sf\implies (-9+(-7))+11=-9+(-7+11)$

$\sf\implies -9-7+11=-9-7+11$

$\sf\implies -16+11=-16+11$

$\sf\implies -5=-5$

$\bf \red{Hence\: verified\:!}$

Answer 2

Answer:

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