Long Question Answer: Simple Equations

Q1. Verify that -(-x)=x for
(i) x = 11/15
(ii) x = -13/17
Ans:
(i) L.H.S =

R.H.S = x = 11/15
∴ L.H.S = R.H.S
Hence, verified.
(ii) L.H.S =
R.H.S = -13/17
∴ L.H.S = R.H.S
 Hence, verified.

Q2. What value of n satisfies the equation  ?
Ans:
Given,


Multiplying both sides by 8 we get,
⇒  7n - 42 = 84
⇒  7n = 84 + 42
⇒  7n = 126
⇒ n = 126/7
⇒ n = 18
∴ The value of n is 18.

Q3. Solve 10x=30 for the value of x.
Ans:
Given, 10x = 30
Divide 10 on both the sides,
⇒ 10x / 10 = 30/10
⇒ x = 3

Q4. State true or false:If we multiply both sides of an equation by zero, then we can create an equivalent equation.
A. True
B. False
Ans:
Let the equation be y = 7
By multiplying zero to both sides, we will get
y × 0 = 7 x 0
0 = 0
Hence, this is a true statement.

Q5. State true or false:The statement "x multiplied by 5 and added to 10" can be represented as 10+5x
A. True
B. False
Ans:
Here, the given statement is x multiplied by 5 and added to 10.
The word 'multiplied by' suggests multiplication that is x multiplied by 5 means x × 5 = 5x and the word 'added to' suggests addition. So, the verbal expression x multiplied by 5 and added to 10 can be represented by the algebraic expression 10 + 5x.
Hence, the statement x multiplied by 5 and added to 10 can be rewritten as 10 + 5x.
So, TRUE

Q6. Solve the following equations : 2+y=7
Ans:
2+y=7
So we get
y = 7 - 2
=5.

Q7. A number subtracted by 30 gives 14 subtracted by 3 times the number. Find the number.
Ans:
Let the number be x.
As per the question, we have
30 - x = 3x - 14
Transpose x on one side,
30 + 14 = 3x + x
4x = 44
x = 11
Therefore, the number is 11.

Q8. Solve the equation: 3y + 39 = 8
Ans:
Given equation : 3y+39=8
3y =8 - 39 (Transporting 39 to RHS)
3y = -31
y = -31 / 3  (Transporting 3 to RHS)
∴ The solution of 3y + 39 = 8 is y = -31/3

Q9. Leela is Radha's younger sister. Leela is 4 years younger than Radha. Can you write Leela's age in terms of Radha's age? Take Radha's age to be x years.
Ans:
Writing Leela's age in terms of Radha's
It is given that, Leela is 4 years younger than Radha
If we assume Radha's age to be x years.
Then Leela's age is found to be (x-4) years.
Hence, Leela's age in terms of Radha's age is (x - 4)  if Radha's age is x.

Q10. The sum of three number is 15. If the second number is subtracted from the sum of first and third number then we get 5 an if twice of first number is added to second and if the third number is subtracted from the sum we get 4.
Ans:
Let the three numbers be a, b, c
The sum of three numbers is 15
⇒ a + b + c = 15 ⋯(1)
The second number is subtracted from the sum of first and third number to geet 5
⇒ a - b + c = 5 ⋯(2)
twice of first number is added to second and if the third number is subtracted from sum we get 4
⇒ 2a + b - c = 4 ⋯(3)
(1) - (2)
⇒ 2b = 10
b = 5
put it in (1)
⇒ a + c = 10
c = 10 - a
put it in (3)
2a + 5 - 10 + a = 4
3a - 5 = 4
3a = 9
a = 3
⇒ c = 10 - 3
c = 7
So, a = 3; b = 5; c = 7

Q11. Solve: 3y + 5 = 44
Ans:
The given equation is 3y+5=44
So,
3y = 44-5
3y = 39
y =  39/3
∴  y = 13

Q12. State true or false: 4x-5=7 does not have an integer as its solution.
A. True
B. False
Ans:
Given linear equation is 4x - 5 = 7
Adding  5 on both sides, we get:
4x - 5 + 5 = 7 + 5
⇒ 4x = 12
Dividing the complete equation by 4, we get:
x = 12/4
x = 3
Hence, the solution of this equation is 3, which is an integer.
Therefore, the given statement is false.

Q13. If the mean of 2,4,6,8,x,y is 5, then find the value of x+y?
(a) 6
(b) 8
(c) 10
(d) 12
Ans: (c)
Mean = Sum of the terms / Total Number of turns
⇒ 2 + 4 + 6 + 8 + x + y / 6 = 5
20 + x + y / 6 = 5
20 + x + y = 5(6)
x + y = 30 - 20
= 10

Q14. 6x - 3 = 4x + 5 is a simple equation give reason
Ans:
Given equation,
⇒ 6x - 3 = 4x + 5
⇒ 6x - 4x = 5 + 3
⇒ 2x = 8
⇒ x = 4
⇒ As above equation has only one variable so it is a simple equation.

Q15. The  sum of the digits of a 2-digit number is 8. When 18 is added to the number, its digits are reversed. Find the number.
Ans:
Let the ten's and unit digit be x and 8/x respectively.
Then,

⇒ 10x² + 18x + 8 = 80 + x²
⇒ 10x²-x² +18x + 8 - 80 = 0
⇒ 9x² +18x - 72 = 0
⇒ x²  + 2x  - 8  = 0
⇒ x² + 4x - 2x - 8 = 0
⇒ x(x + 4) - 2(x + 4) = 0
⇒ x = -4, 2     ∴ x = 2sinθx > 0
⇒ 8/x = 8/2 = 4.
∴ The numbers is 24.