Q1: Solve the following equations:
(a) 10p = 100
Ans:
Now,
We have to divide both of these sides of the equation by 10,
Then, we get,
= 10p/10 = 100/10
= p = 10
(b) 10p + 10 = 100
Ans:
Firstly we have to subtract 10 from both sides of the following equation,
Then, we get,
= 10p + 10 – 10 = 100 – 10
= 10p = 90
Now,
We have to divide both of these sides of the equation by 10,
Then, we get,
= 10p/10 = 90/10
= p = 9
(c) p/4 = 5
Ans:
Now,
We have to multiply both of these sides of the equation by 4,
Then, we get,
= p/4 × 4 = 5 × 4
= p = 20
(d) – p/3 = 5
Ans:
Now,
We have to multiply both of these sides of the equation by – 3,
Then, we receive,
= – p/3 × ( 3) = 5 × ( 3)
= p = – 15
(e) 3p/4 = 6
Ans:
First, we have to multiply both of these sides of the equation by 4,
Then, we get,
= (3p/4) × (4) = 6 × 4
= 3p = 24
Now,
We have to divide both of these sides of the equation by 3,
Then, we get,
= 3p/3 = 24/3
= p = 8
(f) 3s = – 9
Ans:
Now,
We have to divide both of these sides of the equation by 3,
Then, we get,
= 3s/3 = 9/3
= s = 3
(g) 3s + 12 = 0
Ans:
First, we have to subtract the number 12 from the both sides of the equation,
Then, we get,
= 3s + 12 – 12 = 0 – 12
= 3s = 12
Now,
We have to divide both of these sides of the equation by 3,
Then, we get,
= 3s/3 = 12/3
= s = – 4
(h) 3s = 0
Ans:
Now,
We have to divide both of these sides of the equation by 3,
Then, we get,
= 3s/3 = 0/3
= s = 0
(i) 2q = 6
Ans:
Now,
We have to divide both of these sides of the equation by 2,
Then, we get,
= 2q/2 = 6/2
= q = 3
(j) 2q – 6 = 0
Ans:
Firstly we have to add 6 to both the sides of the following equation,
Then, we get,
= 2q – 6 + 6 = 0 + 6
= 2q = 6
Now,
We have to divide both of these sides of the equation by 2,
Then, we get,
= 2q/2 = 6/2
= q = 3
(k) 2q + 6 = 0
Answer :
First, we have to subtract the number 6 from the both sides of the following equation,
Then, we get,
= 2q + 6 – 6 = 0 – 6
= 2q = – 6
Now,
We have to divide both of these sides of the equation by the number 2,
Then, we get,
= 2q/2 = – 6/2
= q = – 3
(l) 2q + 6 = 12
Ans:
First, we have to subtract the number 6 to the both sides of the following equation,
Then, we get,
= 2q + 6 – 6 = 12 – 6
= 2q = 6
Now,
We have to divide both of these sides of the equation by 2,
Then, we get,
= 2q/2 = 6/2
= q = 3
Q2: Solve the following equations:
(a) 2(x + 4) = 12
Ans:
Let us divide both these sides by 2,
= (2(x + 4))/2 = 12/2
= x + 4 = 6
By transposing four from the LHS to RHS, it becomes 4
= x = 6 – 4
= x = 2
(b) 3(n – 5) = 21
Ans:
Let us divide both these sides by 3,
= (3(n – 5))/3 = 21/3
= n – 5 = 7
By transposing 5 from the LHS to the RHS, it becomes 5
= n = 7 + 5
= n = 12
(c) 3(n – 5) = – 21
Ans:
Let us divide both these sides by 3,
= (3(n – 5))/3 = – 21/3
= n – 5 = 7
By transposing 5 from the LHS to the RHS, it becomes 5
= n = – 7 + 5
= n = – 2
(d) – 4(2 + x) = 8
Ans:
Let us divide both these sides by 4,
= (4(2 + x))/ (4) = 8/ (4)
= 2 + x = 2
By transposing two from the LHS to the RHS, it becomes – 2
= x = 2 – 2
= x = – 4
(e) 4(2 – x) = 8
Ans:
Let us divide both these sides by 4,
= (4(2 – x))/ 4 = 8/ 4
= 2 – x = 2
By transposing the number 2 from the LHS to the RHS, it becomes – 2
= – x = 2 – 2
= – x = 0
= x = 0
Q3: (a) Construct 3 equations starting with x = 2
Ans:
First equation is,
Multiply both these side by 6
= 6x = 12 … [equation 1]
Second equation is,
Subtracting the number 4 from both side,
= 6x – 4 = 12 4
= 6x – 4 = 8 … [equation 2]
Third equation is,
Divide both these sides by 6
= (6x/6) – (4/6) = (8/6)
= x – (4/6) = (8/6) … [equation 3]
(b) Construct three equations that start with x = – 2
Ans:
First equation is,
Multiply both these side by 5
= 5x = 10 … [equation 1]
Second equation is,
Subtracting the number 3 from both side,
= 5x – 3 = – 10 – 3
= 5x – 3 = – 13 … [equation 2]
Third equation is,
Dividing both these side by 2
= (5x/2) – (3/2) = (13/2) … [equation 3]
Q4: Solve the following equations:
(a) 2y + (5/2) = (37/2)
Ans:
By transposing the fraction (5/2) from LHS to RHS, so it becomes 5/2
Then,
= 2y = (37/2) – (5/2)
= 2y = (375)/2
= 2y = 32/2
Now,
Divide both the side by the number 2,
= 2y/2 = (32/2)/2
= y = (32/2) × (1/2)
= y = 32/4
= y = 8
(b) 5t + 28 = 10
Answer :
By transposing 28 from the LHS to RHS, it becomes 28
Then,
= 5t = 10 – 28
= 5t = – 18
Now,
Dividing both these sides by 5,
= 5t/5= 18/5
= t = 18/5
(c) (a/5) + 3 = 2
Ans:
By transposing three from the LHS to RHS, it becomes 3
Then,
= a/5 = 2 – 3
= a/5 = – 1
Now,
Multiply both these sides by 5,
= (a/5) × 5= 1 × 5
= a = 5
(d) (q/4) + 7 = 5
Ans:
By transposing the number 7 from the LHS to RHS, it becomes 7
Then,
= q/4 = 5 – 7
= q/4 = – 2
Now,
Multiply both these sides by 4,
= (q/4) × 4= 2 × 4
= a = 8
(e) (5/2) x = 5
Ans:
First, we have to multiply both these sides by 2,
= (5x/2) × 2 = – 5 × 2
= 5x = – 10
Now,
We have to divide both these sides by 5,
Then we get,
= 5x/5 = 10/5
= x = 2
(f) (5/2) x = 25/4
Ans:
First, we have to multiply both these sides by 2,
= (5x/2) × 2 = (25/4) × 2
= 5x = (25/2)
Now,
We have to divide both these sides by 5,
Then we get,
= 5x/5 = (25/2)/5
= x = (25/2) × (1/5)
= x = (5/2)
Q5: Solve the following equations:
(a) 4 = 5(p – 2)
Ans:
Let us divide both these sides by 5,
= 4/5 = (5(p – 2))/5
= 4/5 = p 2
By transposing – 2 from the RHS to the LHS, it becomes 2
= (4/5) + 2 = p
= (4 + 10)/ 5 = p
= p = 14/5
(b) – 4 = 5(p – 2)
Ans:
Let us divide both these sides by 5,
= – 4/5 = (5(p – 2))/5
= – 4/5 = p 2
Now by transposing – 2 from the RHS to the LHS, it becomes 2
= – (4/5) + 2 = p
= ( 4 + 10)/ 5 = p
= p = 6/5
(c) 16 = 4 + 3(t + 2)
Ans:
By transposing four from the RHS to the LHS, it becomes – 4
= 16 – 4 = 3(t + 2)
= 12 = 3(t + 2)
Let us divide both these side by 3,
= 12/3 = (3(t + 2))/ 3
= 4 = t + 2
By transposing 2 from the RHS to the LHS it becomes – 2
= 4 – 2 = t
= t = 2
(d) 4 + 5(p – 1) =34
Ans:
By transposing 4 from the LHS to the RHS it becomes – 4
= 5(p – 1) = 34 – 4
= 5(p – 1) = 30
Let us divide both these side by 5,
= (5(p – 1))/ 5 = 30/5
= p – 1 = 6
By transposing – 1 from the RHS to the LHS it becomes 1
= p = 6 + 1
= p = 7
(e) 0 = 16 + 4(m – 6)
Ans:
By transposing 16 from the RHS to the LHS it becomes – 16
= 0 – 16 = 4(m – 6)
= – 16 = 4(m – 6)
Let us divide both these side by the number 4
= – 16/4 = (4(m – 6))/ 4
= – 4 = m – 6
Now by transposing – 6 from the RHS to the LHS it becomes 6
= – 4 + 6 = m
= m = 2
76 videos345 docs39 tests

1. What are simple equations? 
2. How do you solve simple equations? 
3. Can simple equations have more than one solution? 
4. What is the role of balance in solving simple equations? 
5. How are simple equations useful in reallife situations? 

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