1, Choose the correct one:

i. A number when multiplied by 4 is increased by 54. The number is

a. 21 b. 16 c. 18 d. 19

ii. The length of a rectangle is twice its breadth and its perimeter is 96 m. The length of the rectangle is

a. 28 m b. 30 m c. 32 m d. 36 m

iii. If x/2−x/3 = 5 then x =?

a. 8 b. 16 c. 24 d. 30

iv. Thrice a number when increased by 6 gives 24. The number is

a. 6 b. 7 c. 8 d. 11

v. On adding 9 to the twice of a whole number gives 31. The whole number is

a. 21 b. 16 c. 17 d. 11

2. Solve each of the following equations and check your answers:

a. x – 3 = 5 b. x + 9 = 13 c. x – (3/5) = (7/5) d. x – (1/3) = (2/3)

e. x + (1/2) = (7/2) f. 7 + 4y = -5 g. 2y – (1/2) = (-1/3) h. 3 (x + 6) = 24

3. Solve each of the following equations and check your answers:

a. 3 (x + 2) – 2 (x – 1) = 7

b. 8 (2x – 5) – 6(3x – 7) = 1

c. 6 (1 – 4x) + 7 (2 + 5x) = 53

d. 5 (2 – 3x) -17 (2x -5) = 16

e. (x – 3)/5 -2 = -1

f. 5 (x – 2) + 3 (x +1) = 25

4. Fill in the blanks :

(a) The value of the variable which makes the equations a true statement is called the____________ of the equation.

(b) Any term of an equation may be taken from one side to the other with a change in its sign. This process is called_________________.

(c) An_______________ is a statement of equality which contains one or more unknown variables.

(d) Without changing the equality, we may___________ the same quantity to both side of the equation.

5. Solve each of the following equations. Also, verify the result in each case.

- 6x + 5 = 2x + 17

2. 2 (5x – 3) – 3 (2x – 1) = 9

3. (x/2) = (x/3) + 1.

4. (x/2) + (3/2) = (2x/5) – 1

5. (3/4) (x -1) = (x – 3)

6. 3 (x – 3) = 5 (2x + 1)

7. 3x – 2 (2x -5) = 2 (x + 3) – 8

8. x – (x/4) – (1/2) = 3 + (x/4)

9. (6x – 2)/9 + (3x + 5)/18 = (1/3)

10. m – (m – 1)/2 = 1 – (m – 2)/3

11. (5x – 1)/3 – (2x – 2)/3 = 1

12. 0.6x + 4/5 = 0.28x + 1.16

6. Make equations for given statements :

a. 4 less from thrice a number m is 14.

b. A number x divided by 4 gives 3.

c. 7 less than a number x is 4.

d. Four fifths of a number. is greater than three fourth of the number by 4.

e. x exceeds 3 by 7

7. If 5 is subtracted from three times a number, the result is 16. Find the number.

8. Find the number which when multiplied by 7 is increased by 78.

9. Find three consecutive natural numbers such that the sum of the first and second is 15 more than the third.

10. The difference between two numbers is 7. Six times the smaller plus the larger is 77. Find the numbers.

11. A man says, “I am thinking of a number. When I divide it by 3 and then add 5, my answer is twice the number I thought of”. Find the number.

12. If a number is tripled and the result is increased by 5, we get 50. Find the number.

13. Shikha is 3 years younger to her brother Ravish. If the sum of their ages 37 years, what are their present age?

14. A man 4 times as old as his son. After 16 years, he will be only twice as old as his son. Find their present ages.