Exercise 3.3 (Simple linear equations)

Exercise 3.3

1. Fill in the blanks.

(i) An expression equated to another expression is called equation.

(ii) If a = 5, the value of 2a + 5 is 2(5) + 5 = 10 + 5 = 15.

(iii) The sum of twice and four times of the variable x is 2x and 4x.

2. Say True or False.

(i) Every algebraic expression is an equation (False)

(ii) The expression 7x + 1 can not be reduced without knowing the value of x. (True)

(iii) To add two like terms, its coefficients can be added. (True)

3. Solve:

(i) x + 5 = 8 (ii) p − 3 = 7 (iii) 2x = 30 (iv) m/6 = 5 (v) 7x + 10 = 80

(i) x + 5 = 8

x + 5 – 5 = 8 – 5

x = 3

(ii) p – 3 =7

p – 3 + 3 = 7 + 3

p = 10

(iii) 2x = 20

2x / 2 = 20 / 2

x = 10

(iv) m / 6 = 5

[m/6] × 6 = 5 × 6

m = 30

(v) 7x + 10 = 80

7x + 10 – 10 = 80 – 10

7x = 70

7x / 7 = 70 / 7

x = 10

4. What should be added to 3x + 6y to get 5x + 8y?

5x + 8y – (3x + 6y)

5x + 8y – 3x – 6y

5x – 3x + 8y– 6y

(5 – 3) x + (8 – 6)y

2x + 2y

2x + 2y should be added to 3x + 6y to get 5x + 8y

5. Nine added to thrice a whole number gives 45. Find the number.

Let the whole number be x

3x + 9 = 45

3x + 9 – 9 = 45 – 9

3x = 36

3 / 3 x = 36 / 3

 x = 12

6. Find two consecutive odd numbers whose sum is 200.

Let the two consecutive odd numbers

be x, x + 2

Their sum x + x + 2 = 200

2x + 2 = 200

2x + 2 – 2 = 200 – 2

2x = 198

2x / 2 = 198 / 2

x = 99

x + 2 = 99+ 2 =101

The two consecutive odd numbers are 99, 101.

7. The taxi charges in a city comprise of a fixed charge of ₹ 100 for 5 kms and ₹ 16 per km for every additional km. If the amount paid at the end of the trip was ₹ 740 find the distance travelled.

The distance travelled = x km

Fixed charge for 5 km = ₹ 100

Remaining distance = (x – 5) km

Charge for every additional km = ₹ 16

Charge for (x – 5)km = ₹ (x – 5) 16

Given (x – 5) 16 = ₹ 740 – 100

 = ₹ 640

 (x – 5) x 16 / 16 = 640 / 16 = 40

                  x – 5 = 40

              x – 5 + 5 = 40 + 5

                         x = 45

The distance travelled = 45 km

Objective type questions

8. The generalization of the number pattern 3, 6, 9, 12,… is

(i) n

(ii) 2n

(iii) 3n

(iv) 4n

Answer : (iii) 3n

9. The solution of 3x + 5 = x + 9 is

(i) 2

(ii) 3

(iii) 5

(iv) 4

Answer : (i) 2

10. The equation y + 1 = 0 is true only when y is

(i) 0

(ii) − 1

(iii) 1

(iv) − 2

Answer : (ii) – 1

ANSWERS

EXERCISE-3.3

1. (i) equation (ii) 15 (iii) 6x

2. (i) False (ii) True (iii) True

3. (i) x = 3 (ii) p = 10 (iii) x = 15 (iv) m = 30 (v) x = 10

4. 2x+2y

5. x = 12

6. 99 and 101

7. x = 45km

 Objective type questions

8. (iii) 3n

9. (i) 2

10. (ii) −1