CBSE Class 7 Mathematics Simple Equations Assignment Set 07

Question. Write the following statements in the form of an equation
(i) Five times a number is 45.
(ii) 5 subtracted from two times a number gives 15.
(iii) Thrice a number when added to 15 gives 45.
(iv) A number when divided by 5 gives 15.
(v) The sum of number \( x \) and thrice the number \( y \) is 20.
Answer:
(i) \( 5x = 45 \)
(ii) \( 2x - 5 = 15 \)
(iii) \( 3x + 15 = 45 \)
(iv) \( x \div 5 = 15 \)
(v) \( x + 3y = 20 \)

Question. By trial and error method, find the solution of the following equations
(i) \( x - 3 = 8 \)
(ii) \( 2x + 5 = 15 \)
(iii) \( x + 3 = 5 \)
(iv) \( \frac{1}{2}x + 3 = 14 \)
(v) \( x - 4 = 2x - 5 \)
Answer:
(i) \( x = 11 \)
(ii) \( x = 5 \)
(iii) \( x = 2 \)
(iv) \( x = 22 \)
(v) \( x = 1 \)

Question. Write a statement for the following equations
(i) \( 2x - 5 = 10 \)
(ii) \( x + 5 = 10 \)
(iii) \( 2x + 3 = 7 \)
(iv) \( \frac{x}{2} + 7 = 17 \)
(v) \( \frac{1}{4}x = 2 \)
Answer:
(i) Five subtracted from twice a no. is 10
(ii) Five added to a no. gives 10
(iii) Three added to twice a no. is 7
(iv) Seven added to half a no. gives 17
(v) one fourth of a no. is 2.

Question. Verify whether \( x = 8 \) is a solution of the equation \( 2x - 7 = 9 \) or not ?
Answer: yes

Question. Verify by substitution that
(i) The root of \( 3x - 5 = 7 \) is \( x = 4 \)
(ii) The root of \( 8 - 7y = 1 \) is \( y = 1 \)
Answer:
(i) yes
(ii) yes

Question. If 5 is subtracted from three times a number, the result is 16. Form a simple equation.
Answer: \( 3x - 5 = 16 \)

Question. The sum of a number and its reciprocal is \( \frac{13}{6} \) , Form a simple equation
Answer: \( x + \frac{1}{x} = \frac{13}{6} \)

Question. Form an equation of the following statement
" Sum of two consecutive natural numbers is 3 "
Answer: \( x + (x + 1) = 3 \)

Question. Arun's father is 3 times as old as his son Arun. After 15 years he will be twice the age of his son. Form an equation.
Answer: \( 3x + 15 = 2(x + 15) \)

Question. The length of a rectangle is three times its breadth. If the perimeter of the rectangle is 80 m. Form a simple equation.
Answer: \( 2(x + 3x) = 80 \)