Question

13. The sum of two integers is 65. If one of them is -31, find the other.
14. The difference of an integer a and (-6) is 4. Find the value of a.
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Answer 1

$\large\sf\underline{Question~1\::}$

• The sum of two integers is 65. If one of them is -31, find the other.

‎

$\large\sf\underline{Answer\::}$

• The required other number is $\small{\mathfrak{96}}$.

________________________‎

$\large\bf\underline{Step\:wise~Calculation\::}$

In order to solve this question we would first frame up an equation , and solving the equation we would get our required answer .

Assuming the other integer to be x .

According to the question :

$\sf\:Other~integer~+~(-31) =65$

$\sf\implies\:x+(-31)=65$

$\sf\implies\:x-31=65$

• Transposing -31 to RHS it becomes +31

$\sf\implies\:x=65+31$

$\red{\mid{\fbox{\tt{\:x~=~96}}\mid}}$ ★

‎

$\large\sf\underline{Verifying\::}$

So we got the other number as 96 . Now let's check if it's correct . In order to check we would plug the value of x in the equation framed earlier. Solving that if we get LHS = RHS our answer would be correct. Let's do!

Framed equation : $\sf\:x+(-31)=65$

• Plugging the value of x

$\sf\implies\:96+(-31)=65$

$\sf\implies\:96-31=65$

$\sf\implies\:65=65$

$\bf\implies\:LHS=RHS$

$\small\fbox\blue{Hence~Verified~!!}$

==================

$\large\sf\underline{Question\:2~:}$

• The difference of an integer a and (-6) is 4. Find the value of a.

‎

$\large\sf\underline{Answer\::}$

• The required value of a is $\small{\mathfrak{(-2)}}$.

________________________‎ ‎

‎$\large\bf\underline{Step~wise~Calculation\::}$

In order to calculate the value of a we would frame up the equation following question.

According to the question :

$\sf\:Difference~between~a~and~(-6)~is~4$

• Translating this word problem into equation

$\sf\implies\:a-(-6)=4$

$\sf\implies\:a+6=4$

• Transposing +6 to RHS it becomes -6

$\sf\implies\:a=4-6$

$\red{\mid{\fbox{\tt{a~=~(-2)}}\mid}}$ ★

‎

$\large\sf\underline{Verifying\::}$

So we got the value of a as (-2) . Now let's check if it's correct . In order to check we would plug the value of a in the equation framed earlier. Solving that if we get LHS = RHS our answer would be correct. Let's do!

Framed equation : $\sf\:a-(-6)=4$

• Plugging the value of a

$\sf\implies\:(-2)-(-6)=4$

$\sf\implies\:-2+6=4$

$\sf\implies\:4=4$

$\bf\implies\:LHS=RHS$

$\small\fbox\blue{Hence~Verified~!!}$

___________________________‎

!! Hope it helps !!‎

Answer 2

Correct Question:

The sum of two integers is 65. If òne of them is -31, find the other.

The difference of an integer à and (-6) is 4. Find the value of a.

Answer :-

i⟩ Given that,

• The sum of two integers = 65
• One integer = -31

Assumption:

Let us assume the other integer as (x),

∴ x + (- 31) = 65

⇒ x + (- 31) = 65

⇒ x = 65 + 31

⇒ x = 96

Hence, The integer is 96.

VERIFICATION :-

• x + (- 31) = 65

By putting the value of x in L.H.S :-

⇒ x + (- 31)

⇒ 96 + (- 31)

⇒ 96 - 31

⇒ 65

∴ L.H.S = R.H.S,

Hence, Verified!

⠀⠀⠀⠀⠀___________________

ii⟩ Given that,

The difference of an integer a and (-6) = 4

∴ a + (- 6) = 4

⇒ a + (- 6) = 4

⇒ a = 4 + 6

⇒ a = 10

Hence, The integer a is 10.

VERIFICATION :-

• a + (- 6) = 4

By putting the value of a in L.H.S, :-

⇒ a + (- 6)

⇒ 10 + (- 6)

⇒ 10 - 6

⇒ 4

∴ L.H.S = R.H.S

Hence, Verified!

⠀⠀⠀⠀⠀___________________

Required Answers:-

i⟩ The other integer is 96.

ii⟩ The integer a is 10.