NCERT Class 7 Maths Chapter 4 Simple Equations Exercise 4.1

Chapter 4 Simple Equations Exercise 4.1

Question 1: Complete the last column of the table.

S. No.	Equation	Value	Say, whether the equation is satisfied. (Yes/No)
1	x + 3 = 0	x = 3	= 3 + 3 ≠ 0 Therefore, the equation is not satisfied.
2	x + 3 = 0	x = 0	= 0 + 3 ≠ 0 Therefore, the equation is not satisfied.
3	x + 3 = 0	x = -3	= -3 + 3 = 0 Therefore, the equation is satisfied.
4	x – 7 = 1	x = 7	= 7 - 7 ≠ 1 Therefore, the equation is not satisfied.
5	x – 7 = 1	x = 8	= 8 - 7 = 1 Therefore, the equation is satisfied.
6	5x = 25	x = 0	= 5 x 0 ≠ 25 Therefore, the equation is not satisfied.
7	5x = 25	x = 5	= 5 x 5 = 25 Therefore, the equation is satisfied.
8	5x = 25	x = -5	= 5 x -5 ≠ 25 Therefore, the equation is not satisfied.
9	(m/3) = 2	m = – 6	= -6/2 ≠ 2 Therefore, the equation is not satisfied.
10	(m/3) = 2	m = 0	= 0/3 ≠ 2 Therefore, the equation is not satisfied.
11	(m/3) = 2	m = 6	= 6/2 = 3 Therefore, the equation is satisfied.

Question 2: Check whether the value given in the brackets is a solution to the given equation or not:
(a) n + 5 = 19 (n = 1)
Answer:

LHS	RHS
1 + 5	19
6	19

6 ≠ 19
Therefore, the value n = 1 is not a solution to n + 5 = 19.

(b) 7n + 5 = 19 (n = – 2)
Answer:

LHS	RHS
7 x (-2) + 5 = -14 + 5	19
-9	19

-9 ≠ 19
Therefore, the value n = -2 is not a solution to 7n + 5 = 19.

(c) 7n + 5 = 19 (n = 2)
Answer:

LHS	RHS
7 x 2 + 5 = 14 + 5	19
9	19

9 = 19
Therefore, the value n = 2 is a solution to 7n + 5 = 19.

(d) 4p – 3 = 13 (p = 1)
Answer:

LHS	RHS
4 x 1 - 3	13
1	13

1 ≠ 13
Therefore, the value p = 1 is not a solution to 4p – 3 = 13.

(e) 4p – 3 = 13 (p = – 4)
Answer:

LHS	RHS
4 x (-4) - 3	13
= -16 - 3	13

-19 ≠ 13
Therefore, the value p = -4 is not a solution to 4p – 3 = 13.

(f) 4p – 3 = 13 (p = 0)
Answer:

LHS	RHS
4 x 0 - 3	13
= 0 - 3	13

-3 ≠ 13
Therefore, the value p = 0 is not a solution to 4p – 3 = 13.

Question 3: Solve the following equations by trial and error method:
(i) 5p + 2 = 17
Answer:

p	5p +2	= 17
0	= 5 x 0 + 2 = 0 + 2 = 2	No
1	= 5 x 1 + 2 = 5 + 2 = 7	No
2	= 5 x 2 + 2 = 10 + 2 = 12	No
3	= 5 x 3 + 2 = 15 + 2 = 17	Yes

(ii) 3m – 14 = 4
Answer:

m	3m - 14	= 4
0	= 3 x 0 - 14 = 0 - 14 = -14	No
1	= 3 x 1 - 14 = 3 - 14 = -11	No
2	= 3 x 2 - 14 = 6 - 14 = -8	No
3	= 3 x 3 - 14 = 9 - 14 = -5	No
4	= 3 x 4 - 14 = 12 - 14 = -2	No
5	= 3 x 5 - 14 = 15 - 14 = 1	No
6	= 3 x 6 - 14 = 18 - 14 = 4	Yes

Question 4: Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
Answer: x + 4 = 9

(ii) 2 subtracted from y is 8.
Answer: y - 2 = 8

(iii) Ten times a is 70.
Answer: 10a = 70

(iv) The number b divided by 5 gives 6.
Answer: b/5 = 6

(v) Three-fourth of t is 15.
Answer: 3/4 t = 15

(vi) Seven times m plus 7 gets you 77.
Answer: 7m + 7 =  77

(vii) One-fourth of a number x minus 4 gives 4.
Answer: 1/4 x - 4 = 4

(viii) If you take away 6 from 6 times y, you get 60.
Answer: 6y - 6 = 60

(ix) If you add 3 to one-third of z, you get 30.
Answer: 1/3 z + 3 = 30

Question 5: Write the following equations in statement forms:
(i) p + 4 = 15
Answer: The sum of numbers p and 4 is 15.

(ii) m – 7 = 3
Answer: 7 subtracted from m is 3.

(iii) 2m = 7
Answer: Twice of number m is 7.

(iv) m/5 = 3
Answer: The number m divided by 5 gives 3.

(v) (3m)/5 = 6
Answer: Three-fifth of m is 6.

(vi) 3p + 4 = 25
Answer: Three times p plus 4 gives you 25.

(vii) 4p – 2 = 18
Answer: Four times p minus 2 gives you 18.

(viii) p/2 + 2 = 8
Answer: If you add half of a number p to 2, you get 8.

Question 6: Set up an equation in the following cases:
(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Parmit’s marbles.)
Answer:
Number of marbles Parmit has = m
Irfan has 7 marbles more than five times the marbles Parmit has
= 5 x number of Parmit’s marbles + 7 = Total number of marbles Irfan having
= (5 x m) + 7 = 37
= 5m + 7 = 37

(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi’s age to be y years.)
Answer:
Let Laxmi’s age be = y years old
Laxmi’s father is 4 years older than three times of her age
= 3 x Laxmi’s age + 4 = Age of Laxmi’s father
= (3 x y) + 4 = 49
= 3y + 4 = 49

(iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l.)
Answer:
Highest score in the class = 87
Let the lowest score be l.
= 2 x lowest score + 7 = highest marks in the class
= (2 x l) + 7 = 87
= 2l + 7 = 87

(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees).
Answer:
Let the base angle be b.
Vertex angle = 2 x base angle = 2b
= b + b + 2b = 180°
= 4b = 180°