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NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.1

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NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.1, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.1.

NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.1

Question 1.
Complete the last column of the table.
NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations 1
Solution:
NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations 2

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)
(b) 7n + 5 = 19 (n = – 2)
(c) 7n + 5 = 19 (n = 2)
(d) 4p – 3 = 13 (p = 1)
(e) 4p – 3 = 13 (p = – 4)
(f) 4p – 3 = 13 (p = 0).

Solution:
(a) n + 5 = 19 (n = 1)
L.H.S. = n + 5 = 1 + 5 | when n = 1 = 5
R.H.S. = 19
∵ L.H.S. ≠ R.H.S.
∴ n = 1 is not a solution to the given equation n + 5 = 19.

(b) 7n + 5 = 19 (n = – 2)
L.H.S. = 7n + 5 = 7(- 2) + 5 | when n = – 2 = – 14 + 5 = – 9
R.H.S. = 19
∵ L.H.S. ≠ R.H.S.
∴ n = – 2 is not a solution to the given equation 7n + 5 = 19.

(c) 7n + 5 = 19 (n = 2)
L.H.S. = In + 5 = 7(2) + 5 | when n = 2 = 14 + 5 = 19 = R.H.S.
∴ n = 2 is a solution to the given equation 7n + 5 = 19.

(d) 4p – 3 = 13 (p = 1)
L.H.S. = 4p – 3 = 4(1) – 3 | when p = 1 = 4 – 3 = 1
R.H.S. = 13
∵ L.H.S. ≠ R.H.S.
∴ p = 1 is not a solution to the given equation 4p – 3 = 13.

(e) 4p – 3 = 13 (p = – 4)
L.H.S. = 4p – 3 = 4(- 4) – 3 , | when p = – 4 = – 16 – 3 = – 19
R.H.S. = 13
∵ L.H.S. ≠ R.H.S.
∴ p = – 4 is not a solution to the given equation
4p – 3 = 13.

(f) 4p – 3 = 13 (p = 0)
L.H.S. = 4 (p) – 3 = 4(0) – 3 | when p = 0 = 0 – 3 = – 3
R.H.S. = 13
∵ L.H.S. ≠ R.H.S.
∴ p = 0 is not a solution to the given equation 4p – 3 = 13.

Question 3.
Solve the following equations by trial and error method.

  1. 5p + 2 = 17
  2. 3m – 14 = 4.

Solution:
(i) 5p + 2 = 17
NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations 3
So, p = 3 is the solution of the given equation 5p + 2 = 17.

(ii) 3m – 14 = 4
NCERT Solutions for Class 7 Maths Chapter 4 Simple Equations 4
So, m = 6 is the solution of the given equation 3m – 14 = 4.

Question 4.
Write equations for the following statements.

  1. The sum of numbers x and 4 is 9.
  2. 2 subtracted from y is 8.
  3. Ten times a is 70.
  4. The number b divided by 5 gives 6.
  5. Three-fourth oft is 15.
  6. Seven times m plus 7 gets you 77.
  7. One-fourth of a number x minus 4 gives 4.
  8. If you take away 6 from 6 times y, you get 60.
  9. If you add 3 to one-third of z, you get 30.

Solution:

  1. x + 4 = 9
  2. y – 2 = 8
  3. 10 α = 70
  4. \(\frac { b }{ 5 } \) = 6
  5. \(\frac { 3 }{ 4 } \) t = 15
  6. 7m + 7 = 77
  7. \(\frac { 1 }{ 4 } \) x – 4 = 4
  8. 6y – 6 = 60
  9. \(\frac { 1 }{ 3 } \) z + 3 = 30

Question 5.
Write the following equations in statement forms:

  1. p + 4 = 15
  2. m – 7 = 3
  3. 2m = 7
  4. \(\frac { m }{ 5 } \) = 3
  5. \(\frac { 3m }{ 5 } \) = 6
  6. 3p + 4 = 25
  7. 4p – 2 = 18
  8. \(\frac { p }{ 2 } \) + 2 = 8.

Solution:

  1. The sum of p and 4 is 15.
  2. 7 subtracted from m is 3.
  3. Twice a number m is 7.
  4. One-fifth of a number m is 3.
  5. Three-fifth of a number m is 6.
  6. Three times a numberp when added to 4 gives 25.
  7. 2 subtracted from four times a number p is 18.
  8. Add 2 to half of a number p to get 8.

Question 6.
Set up an equation in the following cases:

  1. 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.)
  2. 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.)
  3. 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.)
  4. 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 triangle is 180 degrees).

Solution:
(i) Let Parmit has m marbles. Then, five times the marbles Parmit has = 5m
Irfan has 7 marbles more than five times the marbles Parmit has = 5m + 7,
i.e., Irfan has (5m + 7) marbles
But it is given that Irfan has 37 marbles. Therefore, 5m + 7 = 37

(ii) Let the age of Laxmi be y years.
Then, three times Laxmi’s age = 3y years Laxmi’s father is 4 years older than three times Laxmi’s age,
i.e., Age of Laxmi’s father = (3y + 4) years But it is given that Laxmi’s father is 49 years old Therefore, 3y + 4 = 49

(iii) Let the lowest marks be l.
Then, twice the lowest marks = 21
Highest score obtained by a student in her class is twice the lowest marks plus 7, i.e.,
Highest score = 2l + 7
But this is given to be 87
Therefore, 2l + 7 = 87

(iv) Let the base angle be b in degrees. Then the vertex angle is 2b in degrees.
∵ Sum of the angles of a triangle is 180 degrees.
∴ 2 b + b + b = 180° or 4 b = 180°

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NCERT Solutions for Class 7 Maths