**Q-1) Mention the first step you will use to separate the variable and then solve the equations:**

**a + 2 = 0****b – 3 = 0****p – 2 = 6****q + 4 = 2****m – 5 = – 8****n – 5 = 5****x + 5 = 5****k + 8 = – 8**

**Ans.) **

1) a + 2 = 0

On Subtracting 2 from L.H.S and R.H.S of the above equation, we get

a + 2 – 2 = 0 – 2

a = – 2

2) b – 3 = 0

On adding 3 to L.H.S and R.H.S of the above equation, we get

b – 3 + 3 = 0 + 3

b = 3

3) p – 2 = 6

On adding 2 to L.H.S and R.H.S of the above equation, we get

p – 2 + 2 = 6 + 2

p = 8

4) q + 4 = 2

On Subtracting 4 from L.H.S and R.H.S of the above equation, we get

q + 4 – 4 = 2 – 4

q = – 2

5) m – 5 = – 8

On adding 5 to L.H.S and R.H.S of the above equation, we get

m – 5 + 5 = – 8 + 5

m = – 3

6) n – 5 = 5

On adding 5 to L.H.S and R.H.S of the above equation, we get

n – 5 + 5 = 5 + 5

n = 10

7) x + 5 = 5

On Subtracting 5 from L.H.S and R.H.S of the above equation, we get

x + 5 – 5 = 5 – 5

x = 0

8) k + 8 = – 8

On Subtracting 8 from L.H.S and R.H.S of the above equation, we get

k + 8 – 8 = – 8 – 8

k = – 16

**Q-2) Mention the first step you have to use to separate the variable and then solve the given equations;**

**4x = 48****y/3 = 5****z/8 = 5****5m = 32****7n = 28****t/4 = 7/3****x/6 = 5/17****40m = – 5**

**Ans.)**

1) 4x = 48

On dividing L.H.S and R.H.S by 4 in the above equation, we get

4x/4 = 48/4

x = 12

2) y/3 = 5

On multiplying L.H.S and R.H.S by 3 in the above equation, we get

(y*3)/3 = 5*3

y = 15

3) z/8 = 5

On multiplying L.H.S and R.H.S by 8 in the above equation, we get

(z*8)/8 = 5*8

z = 40

4) 5m = 32

On dividing L.H.S and R.H.S by 5 in the above equation, we get

5m/5 = 32/5

m = 32/5

5) 7n = 28

On dividing L.H.S and R.H.S by 7 in the above equation, we get

7n/7 = 28/7

n = 4

6) t/4 = 7/3

On multiplying L.H.S and R.H.S by 4 in the above equation, we get

(t*4)/4 = (7*4)/3

t = 28/3

7) x/6 = 5/17

On multiplying L.H.S and R.H.S by 6 in the above equation, we get

(x*6)/6 = (5*6)/17

x = 30/17

8) 40m = – 5

On dividing L.H.S and R.H.S by 40 in the above equation, we get

40m/40 = (- 5)/40

m = – 1/8

**Q-3) Mention the first step you have to use to separate the variable and then solve the given equations;**

**4x – 5 = 48****6y + 9 = 19****40x = 160****5n/8 = 8**

**Ans.)**

1) 4x – 5 = 48

On adding 5 to L.H.S and R.H.S of the above equation, we get

4x – 5 + 5 = 48 + 5

4x = 53

On dividing L.H.S and R.H.S by 4 in the above equation, we get

4x/4 = 53/4

x = 53/4

2) 6y + 9 = 19

On subtracting 9 from L.H.S and R.H.S of the above equation, we get

6y + 9 – 9 = 19 – 9

6y = 10

On dividing L.H.S and R.H.S by 6 in the above equation, we get

4x/4 = 53/4

6y/6 = 10/6

y = 5/3

3) 40x = 160

On dividing L.H.S and R.H.S by 40 in the above equation, we get

40x/40 = 160/40

x = 4

4) 5n/8 = 8

On multiplying L.H.S and R.H.S by 8 of in the above equation, we get

(5*n*8)/8 = 8*8

5n = 64

On dividing L.H.S and R.H.S by 5 in the above equation, we get

5n/5 = 64/5

n = 64/5

**Q-4) Solve the equations given below:**

**20x = 400****15y + 15 = 150****m/5 = 6****-3x/4 = 4****4m/5 = 7****5n = 25****4k + 10 = 0****4t = 0****3n = 12****4y – 12 = 0****3m + 9 = 0****3m + 9 = 18**

**Ans.)**

1) 20x = 400

On dividing L.H.S and R.H.S by 20 in the above equation, we get

20x/20 = 400/20

x = 20

2) 15y + 15 = 150

On subtracting 15 from L.H.S and R.H.S of the above equation, we get

15y + 15 – 15 = 150 – 15

15y = 135

On dividing L.H.S and R.H.S by 15 in the above equation, we get

15y/15 = 135/15

y = 9

3) m/5 = 6

On multiplying L.H.S and R.H.S by 5 in the above equation, we get

(m*5)/5 = 6*5

m = 30

4) -3x/4 = 4

On multiplying L.H.S and R.H.S by 4 of in the above equation, we get

(-3x*4)/4 = 4*4

– 3x = 16

On dividing L.H.S and R.H.S by (- 3) in the above equation, we get

(-3x) / (-3) = 16/(-3)

x = – 16/3

5) 4m/5 = 7

On multiplying L.H.S and R.H.S by 5 in the above equation, we get

(4m*5)/5 = 7*5

4m = 35

On dividing L.H.S and R.H.S by 4 in the above equation, we get

(4m)/4 = 35/4

m = 35/4

6) 5n = 25

On dividing L.H.S and R.H.S by 5 in the above equation, we get

5n/5 = 25/5

n = 5

7) 4k + 10 = 0

On subtracting 10 from L.H.S and R.H.S of the above equation, we get

4k + 10 – 10 = 0 – 10

4k = – 10

On dividing L.H.S and R.H.S by 4 in the above equation, we get

(4k)/4 = (-10)/4

k = – 10/4

8) 4t = 0

On dividing L.H.S and R.H.S by 4 in the above equation, we get

4t/4 = 0/4

t = 0

9) 3n = 12

On dividing L.H.S and R.H.S by 3 in the above equation, we get

3n/3 = 12/3

n = 4

10) 4y – 12 = 0

On adding 12 to L.H.S and R.H.S of the above equation, we get

4y – 12 + 12 = 0 + 12

4y = 12

On dividing L.H.S and R.H.S by 4 in the above equation, we get

4y/4 = 12/4

y = 3

11) 3m + 9 = 0

On subtracting 9 from L.H.S and R.H.S of the above equation, we get

3m + 9 – 9 = 0 – 9

3m = – 9

On dividing L.H.S and R.H.S by 3 in the above equation, we get

3m/3 = (-9)/3

m = – 3

12) 3m + 9 = 18

On subtracting 9 from L.H.S and R.H.S of the above equation, we get

3m + 9 – 9 = 18 – 9

3m = 9

On dividing L.H.S and R.H.S by 3 in the above equation, we get

3m/3 = 9/3

m = 3