## Chapter 4 Simple Equations Exercise 4.2

**Question 1: Give first the step you will use to separate the variable and then solve the equation:(a) x – 1 = 0 Answer:**

Adding 1 on both the sides

=

*x*- 1 + 1 = 0 + 1

=

*x*= 1

So,

*x*= 1.

**(b) x + 1 = 0**

Answer:

Answer:

Subtracting 1 on both the sides

=

*x*+ 1 - 1 = 0 - 1

=

*x*= -1

So,

*x*= -1.

**(c) x – 1 = 5**

Answer:

Adding 1 on both the sides

Answer:

=

*x*- 1 + 1 = 5 + 1

=

*x*= 6

So,

*x*= 6.

(d) x + 6 = 2

Answer:

(d) x + 6 = 2

Answer:

Subtracting 6 on both the sides

=

*x*+ 6 - 6 = 2 - 6

=

*x*= -4

So,

*x*= -4.

**(e) y – 4 = – 7**

Answer:

Answer:

Adding 4 on both the sides

=

*y*- 4 + 4 = -7 + 4

=

*y*= -3

So,

*y*= -3.

**(f) y – 4 = 4**

Answer:

Answer:

Adding 4 on both the sides

=

*y*- 4 + 4 = 4 + 4

=

*y*= 8

So,

*y*= 8.

**(g) y + 4 = 4**

Answer:

Answer:

Subtracting 4 on both the sides

=

*y*+ 4 - 4 = 4 - 4

=

*y*= 0

So,

*y*= 4.

**(h) y + 4 = – 4**

Answer:

Answer:

Subtracting 4 on both the sides

=

*y*+ 4 - 4 = -4 - 4

=

*y*= -8

So,

*y*= -8.

**Question 2: Give first the step you will use to separate the variable and then solve the equation:**

(a) 3l = 42

Answer:

(a) 3l = 42

Answer:

Dividing 3 on both the sides

= 3

*l*/3 = l = 42/3 = 14

So,

*l*= 14.

**(b) b/2 = 6**

Answer:

Answer:

Multiplying 2 on both the sides

=

*b*/2 x 2 =

*b*= 6 x 2 = 12

So,

*b*= 12.

**(c) p/7 = 4**

Answer:

Answer:

Multiplying 7 on both the sides

=

*p*/7 x 7 = 4 x 7 =

*p*= 28

So,

*p*= 28.

**(d) 4x = 25**

Answer:

Answer:

Dividing 4 on both the sides

= 4

*x*/4 = 25/4 =

*x*= 25/4

So,

*x*= 25/4.

**(e) 8y = 36**

Answer:

Answer:

Dividing 8 on both the sides

= 8

*y*/8 = 36/8 =

*y*= 4

So,

*y*= 4.

**(f) (z/3) = (5/4)**

Answer:

Answer:

Multiplying 3 on both the sides

=

*z*/3 x 3 = 5/4 x 3 =

*z*= 15/4

So,

*z*= 15/4.

(g) (a/5) = (7/15)

Answer:

(g) (a/5) = (7/15)

Answer:

Multiplying 5 on both the sides

=

*a*/5 x 5 = 7/15 x 5 =

*a*= 35/15 = 7/3

So,

*a*= 7/3.

(h) 20t = – 10

Answer:

(h) 20t = – 10

Answer:

Dividing 20 on both the sides

= 20

*t*/20 = -10/20 =

*t*= -1/2

So,

*t*= 1/-2.

**Question 3: Give the steps you will use to separate the variable and then solve the equation:**

(a) 3n – 2 = 46

Answer:

(a) 3n – 2 = 46

Answer:

Adding 2 on both the sides

= 3

*n*- 2 + 2 = 46 + 2

= 3

*n*= 48

Dividing 3 on both the sides

= 3

*n*/3 = 48/3 =

*n*= 16

So,

*n*= 16.

(b) 5m + 7 = 17

Answer:

(b) 5m + 7 = 17

Answer:

Subtracting 7 on both the sides

= 5

*m*+ 7 - 7 = 17 - 7

= 5

*m*= 10

Dividing 5 on both the sides

= 5

*m*/5 = 10/5 =

*m*= 2

So,

*m*= 2.

**(c) 20p/3 = 40**

Answer:

Answer:

Multiplying 3 on both the sides

= 20

*p*/3 x 3 = 40 x 3 = 20

*p*= 120

Dividing 20 on both the sides

= 20

*p*/20 = 120/20 =

*p*= 60

So,

*p*= 60.

(d) 3p/10 = 6

Answer:

(d) 3p/10 = 6

Answer:

Multiplying 10 on both the sides

= 3

*p*/10 x 10 = 6 x 10 = 3

*p*= 60

Dividing 3 on both the sides

= 3

*p*/3 = 60/3 = 20

So,

*p*= 20.

Question 4: Solve the following equations:

(a) 10p = 100

Answer:

Question 4: Solve the following equations:

(a) 10p = 100

Answer:

Dividing 10 on both the sides

= 10

*p*/10 = 100/10 =

*p*= 10

So,

*p*= 10.

**(b) 10p + 10 = 100**

Answer:

Answer:

Subtracting 10 on both the sides

= 10

*p*+ 10 - 10 = 100 - 10

= 10

*p*= 90

Dividing 10 on both the sides

= 10

*p*/10 = 90/10 =

*p*= 9

So,

*p*= 9.

**(c) p/4 = 5**

Answer:

Answer:

Multiplying 4 on both the sides

=

*p*/4 x 4 = 5 x 4 =

*p*= 20

So,

*p*= 20.

(d) - p/3 = 5

Answer:

(d) - p/3 = 5

Answer:

Multiplying -3 on both the sides

=

*p*/-3 x -3 = 5 x -3 =

*p*= -15

So,

*p*= -15.

(e) 3p/4 = 6

Answer:

(e) 3p/4 = 6

Answer:

Multiplying 4 on both the sides

= 3

*p*/4 x 4 = 6 x 4

= 3

*p*= 24

Dividing 3 on both the sides

= 3

*p*/3 = 24/3 =

*p*= 8

So,

*p*= 8

*.*

(f) 3s = – 9

Answer:

(f) 3s = – 9

Answer:

Dividing 3 on both the sides

= 3

*s*/3 = -9/3 =

*s*= -3

So,

*s*= -3.

**(g) 3s + 12 = 0**

Answer:

Answer:

Subtracting 12 on both the sides

= 3

*s*+ 12 - 12 = 0 - 12

= 3

*s*= -12

Dividing 3 on both the sides

= 3

*s*/3 = -12/3 =

*s*= -4

So,

*s*= -4.

**(h) 3s = 0**

Answer:

Answer:

Dividing 3 on both the sides

= 3

*s*/3 = 0/3 =

*s*= 0

So,

*s*= 0.

**(i) 2q = 6**

Answer:

Answer:

Dividing 2 on both the sides

= 2

*q*/2 = 6/2 =

*q*= 3

So,

*q*= 3.

(j) 2q – 6 = 0

Answer:

(j) 2q – 6 = 0

Answer:

Adding 6 on both the sides

= 2

*q*- 6 + 6 = 0 + 6 = 2

*q*= 6

Dividing 2 on both the sides

= 2

*q*/2 = 6/2 =

*q*= 3

So,

*q*= 3.

(k) 2q + 6 = 0

Answer:

(k) 2q + 6 = 0

Answer:

Subtracting 6 on both the sides

= 2

*q*+ 6 - 6 = 0 - 6 = 2

*q*= -6

Dividing 2 on both the sides

= 2

*q*/2 = -6/2 =

*q*= -3

**(l) 2q + 6 = 12**

Answer:

Answer:

Subtracting 6 on both the sides

= 2

*q*+ 6 - 6 = 12 - 6 = 2

*q*= 6

Dividing 2 on both the sides

= 2

*q*/2 = 6/2 =

*q*= 3

So,

*q*= 3.

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