NCERT Solutions for Class 7 Maths
Chapter 4 Simple Equations
Exercise 4.3
1. Solve the following equations:
(a) 2y + (5/2) = (37/2)
(b) 5t + 28 = 10
(c) (a/5) + 3 = 2
(d) (q/4) + 7 = 5
(e) (5/2) x = -5
(f) (5/2) x = 25/4
(g) 7m + (19/2) = 13
(h) 6z + 10 = – 2
(i) (3/2) l = 2/3
(j) (2b/3) – 5 = 3
☛ Here, to solve given equations, separate the variable on LHS by applying suitable operation and apply same operation on RHS, also to get required solution
(a) 2y + (5/2) = (37/2)
Answer
By transposing (5/2) from LHS to RHS it becomes -5/2
Then,
= 2y = (37/2) – (5/2)
= 2y = (37-5)/2
= 2y = 32/2
Now, divide both side by 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 LHS to RHS it becomes -28
Then,
= 5t = 10 – 28
= 5t = – 18
Now, divide both side by 5,
= 5t/5= -18/5
= t = -18/5
(c) (a/5) + 3 = 2
Answer
By transposing 3 from LHS to RHS it becomes -3
Then,
= a/5 = 2 – 3
= a/5 = – 1
Now, multiply both side by 5,
= (a/5) × 5= -1 × 5
= a = -5
(d) (q/4) + 7 = 5
Answer
By transposing 7 from LHS to RHS it becomes -7
Then,
= q/4 = 5 – 7
= q/4 = – 2
Now,
Multiply both side by 4,
= (q/4) × 4= -2 × 4
= a = -8
(e) (5/2) x = -5
Answer
First we have to multiply both the side by 2,
= (5x/2) × 2 = – 5 × 2
= 5x = – 10
Now, we have to divide both the side by 5,
Then we get,
= 5x/5 = -10/5
= x = -2
(f) (5/2) x = 25/4
Answer
First we have to multiply both the side by 2,
= (5x/2) × 2 = (25/4) × 2
= 5x = (25/2)
Now, we have to divide both the side by 5,
Then we get,
= 5x/5 = (25/2)/5
= x = (25/2) × (1/5)
= x = (5/2)
(g) 7m + (19/2) = 13
Answer
By transposing (19/2) from LHS to RHS it becomes -19/2
Then,
= 7m = 13 – (19/2)
= 7m = (26 – 19)/2
= 7m = 7/2
Now, divide both side by 7,
= 7m/7 = (7/2)/7
= m = (7/2) × (1/7)
= m = ½
(h) 6z + 10 = – 2
Answer
By transposing 10 from LHS to RHS it becomes – 10
Then,
= 6z = -2 – 10
= 6z = – 12
Now, divide both side by 6,
= 6z/6 = -12/6
= m = – 2
(i) (3/2) l = 2/3
Answer
First we have to multiply both the side by 2,
= (3l/2) × 2 = (2/3) × 2
= 3l = (4/3)
Now, we have to divide both the side by 3,
Then we get,
= 3l/3 = (4/3)/3
= l = (4/3) × (1/3)
= x = (4/9)
(j) (2b/3) – 5 = 3
Answer
By transposing -5 from LHS to RHS it becomes 5|
Then,
= 2b/3 = 3 + 5
= 2b/3 = 8
Now, multiply both side by 3,
= (2b/3) × 3= 8 × 3
= 2b = 24
And, divide both side by 2,
= 2b/2 = 24/2
= b = 12
2. Solve the following equations:
(a) 2(x + 4) = 12 (b) 3(n – 5) = 21 (c) 3(n – 5) = – 21
(d) – 4(2 + x) = 8 (e) 4(2 – x) = 8
Answer
(a) 2(x + 4) = 12
Let us divide both the side by 2,
= (2(x + 4))/2 = 12/2
= x + 4 = 6
By transposing 4 from LHS to RHS it becomes -4
= x = 6 – 4
= x = 2
(b) 3(n – 5) = 21
Let us divide both the side by 3,
= (3(n – 5))/3 = 21/3
= n – 5 = 7
By transposing -5 from LHS to RHS it becomes 5
= n = 7 + 5
= n = 12
(c) 3(n – 5) = – 21
Let us divide both the side by 3,
= (3(n – 5))/3 = – 21/3
= n – 5 = -7
By transposing -5 from LHS to RHS it becomes 5
= n = – 7 + 5
= n = – 2
(d) – 4(2 + x) = 8
Let us divide both the side by -4,
= (-4(2 + x))/ (-4) = 8/ (-4)
= 2 + x = -2
By transposing 2 from LHS to RHS it becomes – 2
= x = -2 – 2
= x = – 4
(e) 4(2 – x) = 8
Let us divide both the side by 4,
= (4(2 – x))/ 4 = 8/ 4
= 2 – x = 2
By transposing 2 from LHS to RHS it becomes – 2
= – x = 2 – 2
= – x = 0
= x = 0
3. Solve the following equations:
(a) 4 = 5(p – 2) (b) – 4 = 5(p – 2) (c) 16 = 4 + 3(t + 2)
(d) 4 + 5(p – 1) =34 (e) 0 = 16 + 4(m – 6)
(a) 4 = 5(p – 2)
Let us divide both the side by 5,
= 4/5 = (5(p – 2))/5
= 4/5 = p -2
By transposing – 2 from RHS to LHS it becomes 2
= (4/5) + 2 = p
= (4 + 10)/ 5 = p
= p = 14/5
(b) – 4 = 5(p – 2)
Let us divide both the side by 5,
= – 4/5 = (5(p – 2))/5
= – 4/5 = p -2
By transposing – 2 from RHS to LHS it becomes 2
= – (4/5) + 2 = p
= (- 4 + 10)/ 5 = p
= p = 6/5
(c) 16 = 4 + 3(t + 2)
By transposing 4 from RHS to LHS it becomes – 4
= 16 – 4 = 3(t + 2)
= 12 = 3(t + 2)
Let us divide both the side by 3,
= 12/3 = (3(t + 2))/ 3
= 4 = t + 2
By transposing 2 from RHS to LHS it becomes – 2
= 4 – 2 = t
= t = 2
(d) 4 + 5(p – 1) =34
By transposing 4 from LHS to RHS it becomes – 4
= 5(p – 1) = 34 – 4
= 5(p – 1) = 30
Let us divide both the side by 5,
= (5(p – 1))/ 5 = 30/5
= p – 1 = 6
By transposing – 1 from RHS to LHS it becomes 1
= p = 6 + 1
= p = 7
(e) 0 = 16 + 4(m – 6)
By transposing 16 from RHS to LHS it becomes – 16
= 0 – 16 = 4(m – 6)
= – 16 = 4(m – 6)
Let us divide both the side by 4,
= – 16/4 = (4(m – 6))/ 4
= – 4 = m – 6
By transposing – 6 from RHS to LHS it becomes 6
= – 4 + 6 = m
= m = 2
4. (a) Construct 3 equations starting with x = 2
(b) Construct 3 equations starting with x = – 2
Answer
(a) Construct 3 equations starting with x = 2
First equation is,
Multiply both side by 6
= 6x = 12 … [equation 1]
Second equation is,
Subtracting 4 from both side,
= 6x – 4 = 12 -4
= 6x – 4 = 8 … [equation 2]
Third equation is,
Divide both side by 6
= (6x/6) – (4/6) = (8/6)
= x – (4/6) = (8/6) … [equation 3]
(b) Construct 3 equations starting with x = – 2
First equation is,
Multiply both side by 5
= 5x = -10 … [equation 1]
Second equation is,
Subtracting 3 from both side,
= 5x – 3 = – 10 – 3
= 5x – 3 = – 13 … [equation 2]
Third equation is,
Dividing both sides by 2
= (5x/2) – (3/2) = (-13/2) … [equation 3]