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

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 4 Simple Equations Ex 4.1 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 4 Simple Equations Ex 4.1

Question 1.
Complete the last column of the table:

Answer:

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:
n + 5 = 19 (n = 1)
L.H.S. = n + 5 = 1 + 5 = 6
R.H.S. = 19
∵ L.H.S. ≠ R.H.S.
∴ n = 1 is not a solution of n + 5 = 19

(b) 7n + 5 = 19 (n = - 2)
Answer:
7n + 5 =19 (n = - 2)
L.H.S. = 7n + 5 = 7(- 2) + 5
= -14 + 5 = - 9
R.H.S. = 19
∵ L.H.S. ≠ R.H.S.
∴ n = - 2 is not a solution of 7n + 5 = 19

(c) 7n + 5 = 19 (n = 2)
Answer:
7n + 5 = 19 (n = 2)
L.H.S. = 7n + 5 = 7(2) + 5
= 14 + 5 = 19
R.H.S. = 19
∵ L.H.S. ≠ R.H.S.
∴ n = 2 is a solution of 7n + 5 = 19

(d) 4p - 3 = 13 (p = 1)
Answer:
4p - 3 =13
(p = 1)
L.H.S. = 4p - 3 = 4(1) - 3 = 4 - 3 = 1
R.H.S. = 13
∵ L.H.S. ≠ R.H.S.
∴ p = 1 is not a solution of 4p - 3 = 13

(e) 4p - 3 = 13 (p = - 4)
Answer:
4p - 3 = 13 (p = - 4)
L.H.S. = 4p - 3 = 4(- 4) - 3
= - 16 - 3 = - 19
R.H.S. = 13
∵ L.H.S. ≠ R.H.S.
∴ p = - 4 is not a solution of 4p - 3 = 13

(f) 4p - 3 = 13 (p = 0)
Answer:
4p - 3 = 13 (p = 0)
L.H.S. = 4p - 3 = 4(0)- 3 = 0-3 = -3
R.H.S. = 13
∵ L.H.S. ≠ R.H.S.
∴ p = 0 is not a solution of 4p - 3 = 13

Question 3.
Solve the following equations by trial and error method :
(i) 5p + 2 = 17
(ii) 3m - 14 = 4
Answer:
(i) 5p + 2 = 17

∴ p = 3 is the solution of equation 5p + 2 = 17.

(ii) 3m - 14 = 4

∴ m = 6 is the solution of equation 3m - 14 = 4.

Question 4.
Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30. •
Answer:
(i) x + 4 = 9
(ii) y - 2 = 8
(iii) 10a = 70
(iv) \(\frac{b}{5}\) = 6
(v) \(\frac{3}{4}\)t = 15
(vi) 7m + 7 = 77
(vii) \(\frac{x}{4}\) - 4 = 4
(viii) 6y - 6 = 60
(ix) \(\frac{1}{3}\)z + 3 = 30

Question 5.
Write the following equations in statement forms:
(i) p + 4 = 15
(ii) m - 7 = 3
(iii) 2m = 7
(iv) \(\frac{m}{5}\) = 3
(v) \(\frac{3 m}{5}\) = 6
(vi) 3p + 4 = 25
(vii) 4p - 2 = 18
(viii) \(\frac{p}{2}\) +2 = 8
Answer:
(i) Sum of numbers p and 4 is 15.
(ii) Difference of numbers m and 7 is 3.
(iii) Two times m is 7.
(iv) One-fifth of a number m is 3.
(v) Three-fifth of a number m is 6.
(vi) Three times p plus 4 is 25.
(vii) Four times p minus 2 is 18.
(viii) Half of a number p plus 2 is 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.)
(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).
(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.)
(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:
(i) Let Parmit has m marbles.
Then five times the marble Parmithas = 5m. Irfan has seven marbles more than Parmit = 5m + 7.
Since, it is given that the total number of marbles Irfan has is 37.
∴ 5m + 7 = 37

(ii) Let the age of Laxmi be y years.
Three times Laxmi’s age is 3y years. Laxmi's father is 4 years older than three times Laxmi's age is so, age of Laxmi's father = 3y + 4 years.
But, the age of Laxmi’s father is 49.
∴ 3y + 4 = 49

(iii) Let the lowest marks be l.
Twice the lowest marks is 2l.
Highest score obtained by a student is twice the lowest marks plus 7 = 2l + 7.
But, the highest marks is 87.
∴ 2l + 7 = 87.

(iv) Let the base angle be b in degrees. Then the vertex angle is 2b in degrees.
Sum of angles of a triangle is 180°.
∴ 2b + b + b = 180°
or 46 = 180°