Class – 7 CH-4 SIMPLE EQUATIONS MATHS NCERT SOLUTIONS

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📐 Class 7 - Chapter 4
Simple Equations

📘 NCERT Mathematics Solutions

📖 Exercise 4.1

Question 1

Complete the last column of the table:

S.No.	Equation	Value	Satisfied? (Yes/No)
(i)	x + 3 = 0	x = 3	No
(ii)	x + 3 = 0	x = 0	No
(iii)	x + 3 = 0	x = -3	Yes
(iv)	x - 7 = 1	x = 7	No
(v)	x - 7 = 1	x = 8	Yes
(vi)	5x = 25	x = 0	No
(vii)	5x = 25	x = 5	Yes
(viii)	5x = 25	x = -5	No
(ix)	m/3 = 2	m = -6	No
(x)	m/3 = 2	m = 0	No
(xi)	m/3 = 2	m = 6	Yes

Question 2

Check whether the value given in brackets is a solution:

(a) n + 5 = 19 (n = 1) → 1 + 5 = 6 ≠ 19 ❌
(b) 7n + 5 = 19 (n = -2) → 7(-2)+5 = -14+5 = -9 ≠ 19 ❌
(c) 7n + 5 = 19 (n = 2) → 14+5 = 19 ✅
(d) 4p - 3 = 13 (p = 1) → 4-3 = 1 ≠ 13 ❌
(e) 4p - 3 = 13 (p = -4) → -16-3 = -19 ≠ 13 ❌
(f) 4p - 3 = 13 (p = 0) → 0-3 = -3 ≠ 13 ❌

Question 3

Solve by trial and error method:

(i) 5p + 2 = 17
p = 3 → 5×3 + 2 = 15+2 = 17 ✅ p = 3

(ii) 3m - 14 = 4
m = 6 → 3×6 - 14 = 18-14 = 4 ✅ m = 6

Question 4

Write equations for the statements:

(i) x + 4 = 9    (ii) y - 2 = 8    (iii) 10a = 70    (iv) b/5 = 6
(v) ¾ t = 15    (vi) 7m + 7 = 77    (vii) x/4 - 4 = 4    (viii) 6y - 6 = 60
(ix) z/3 + 3 = 30

Question 5

Write equations in statement form:

(i) Sum of p and 4 is 15    (ii) 7 subtracted from m is 3    (iii) Two times m is 7
(iv) m divided by 5 gives 3    (v) Three-fifth of m is 6    (vi) Three times p plus 4 is 25
(vii) 4 times p minus 2 is 18    (viii) Half of p plus 2 is 8

Question 6

Set up equations:

(i) 5m + 7 = 37    (ii) 3y + 4 = 49    (iii) 2l + 7 = 87    (iv) 2b + b + b = 180° → 4b = 180°

📖 Exercise 4.2

Question 1

Solve: x - 1 = 0 → x = 1 | x + 1 = 0 → x = -1 | x - 1 = 5 → x = 6

x + 6 = 2 → x = -4 | y - 4 = -7 → y = -3 | y - 4 = 4 → y = 8 | y + 4 = 4 → y = 0 | y + 4 = -4 → y = -8

Question 2

3l = 42 → l = 14 | b/2 = 6 → b = 12 | p/7 = 4 → p = 28 | 4x = 25 → x = 25/4 = 6.25
8y = 36 → y = 4.5 | z/3 = 5/4 → z = 15/4 = 3.75 | a/5 = 7/15 → a = 7/3 | 20t = -10 → t = -0.5

Question 3

3n - 2 = 46 → 3n = 48 → n = 16 | 5m + 7 = 17 → 5m = 10 → m = 2
20p/3 = 40 → 20p = 120 → p = 6 | 3p/10 = 6 → 3p = 60 → p = 20

Question 4

(a) 10p = 100 → p = 10 | (b) 10p + 10 = 100 → 10p = 90 → p = 9
(c) p/4 = 5 → p = 20 | (d) -p/3 = 5 → p = -15 | (e) 3p/4 = 6 → 3p = 24 → p = 8
(f) 3s = -9 → s = -3 | (g) 3s + 12 = 0 → 3s = -12 → s = -4 | (h) 3s = 0 → s = 0
(i) 2q = 6 → q = 3 | (j) 2q - 6 = 0 → 2q = 6 → q = 3 | (k) 2q + 6 = 0 → 2q = -6 → q = -3
(l) 2q + 6 = 12 → 2q = 6 → q = 3

📖 Exercise 4.3

Question 1

(a) 2y + 5/2 = 37/2 → 2y = 16 → y = 8 | (b) 5t + 28 = 10 → 5t = -18 → t = -18/5
(c) a/5 + 3 = 2 → a/5 = -1 → a = -5 | (d) q/4 + 7 = 5 → q/4 = -2 → q = -8
(e) 5x/2 = 10 → 5x = 20 → x = 4 | (f) 5x/2 = 25/4 → 5x = 25/2 → x = 2.5
(g) 7m + 19/2 = 13 → 7m = 7/2 → m = 0.5 | (h) 6z + 10 = -2 → 6z = -12 → z = -2
(i) 3l/2 = 2/3 → 3l = 4/3 → l = 4/9 | (j) 2b/3 - 5 = 3 → 2b/3 = 8 → b = 12

Question 2

(a) 2(x+4)=12 → x+4=6 → x=2 | (b) 3(n-5)=21 → n-5=7 → n=12
(c) 3(n-5)=-21 → n-5=-7 → n=-2 | (d) 3-2(2-y)=7 → -4+2y=4 → 2y=8 → y=4
(e) -4(2-x)=9 → -8+4x=9 → 4x=17 → x=4.25 | (f) 4(2-x)=9 → 8-4x=9 → -4x=1 → x=-0.25
(g) 4+5(p-1)=34 → 5(p-1)=30 → p-1=6 → p=7
(h) 34-5(p-1)=4 → -5(p-1)=-30 → p-1=6 → p=7

Question 3

(a) 4=5(p-2) → 4=5p-10 → 5p=14 → p=2.8
(b) -4=5(p-2) → -4=5p-10 → 5p=6 → p=1.2
(c) -16=-5(2-p) → -16=-10+5p → 5p=-6 → p=-1.2
(d) 10=4+3(t+2) → 6=3(t+2) → t+2=2 → t=0
(e) 28=4+3(t+5) → 24=3(t+5) → t+5=8 → t=3
(f) 0=16+4(m-6) → -16=4(m-6) → m-6=-4 → m=2

Question 4

(a) Starting with x = 2:
① 5x = 10 | ② 5x + 3 = 13 | ③ 5x - 3 = 7

(b) Starting with x = -2:
① 3x = -6 | ② 3x + 7 = 1 | ③ 3x + 10 = 4

📖 Exercise 4.4

Question 1

(a) 8x + 4 = 60 → 8x = 56 → x = 7
(b) y/5 - 4 = 3 → y/5 = 7 → y = 35
(c) 3z/4 + 3 = 21 → 3z/4 = 18 → 3z = 72 → z = 24
(d) 2x - 11 = 15 → 2x = 26 → x = 13
(e) 50 - 3m = 8 → 3m = 42 → m = 14
(f) (n + 19)/5 = 8 → n + 19 = 40 → n = 21
(g) 5x/2 - 7 = 11/2 → 5x/2 = 25/2 → 5x = 25 → x = 5

Question 2

(a) 2y + 7 = 87 → 2y = 80 → y = 40 (Lowest score)
(b) Base angles = b, Vertex angle = 40°, b + b + 40 = 180 → 2b = 140 → b = 70°
(c) Rahul's score = x, Sachin's score = 2x, x + 2x = 198 → 3x = 198 → x = 66, Sachin = 132

Question 3

(i) 5m + 7 = 37 → 5m = 30 → m = 6 marbles
(ii) 3y + 4 = 49 → 3y = 45 → y = 15 years
(iii) t + (3t + 2) = 102 → 4t + 2 = 102 → 4t = 100 → t = 25 fruit trees

Question 4 (Riddle)

"I am a number, take me seven times over, add a fifty, to reach a triple century, you still need forty!"

Let number = n → 7n + 50 + 40 = 300 → 7n + 90 = 300 → 7n = 210 → n = 30

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📐 Class 7 Maths - Simple Equations (NCERT Solutions) | Exercises 4.1 - 4.4