Exercise 2.1

1. Solve the following Simple Equations:

(i) 6m = 12

Solution:

Let's solve for m in the equation 6m = 12

To isolate m, both sides by 6

6m ÷ 6 = 12 ÷ 6

m =

Therefore, m = 2.

Substituting: 6m = 12 i.e. 6(2) = 12

= 12

So, we have found the solution as the equation has been satisfied.

ii. 14p = – 42

Solution:

To isolate p, divide both sides by .

14p ÷ 14 = -42 ÷ 14

=

Therefore, p = -3.

Substituting: 14p = -42

i.e. 14(-3) = -42

= -42

iii. – 5y = 30

Solution:

To isolate y, divide both sides by

-5y ÷ (-5) = 30 ÷ (-5)

Simplifying: y =

Therefore, y = -6

Substituting: -5y = 30 i.e. -5(-6) = 30

= 30

iv –2x = – 12

Solution:

To isolate x, divide both sides by

-2x ÷ (-2) = -12 ÷ (-2)

Simplifying:

x =

Therefore, x = 6.

Substituting: -2x = -12

-2(6) = -12

= -12

v. 34x = – 51

Solution:

To isolate x, divide both sides by

4x ÷ 4 = -51 ÷ 4

Simplifying: x =

Therefore, x = -12.75.

Substituting:

4x = -51

4(-12.75) = -51

= -51

vi. n7 = -3

Solution:

To isolate n, multiply both sides by

n7 × 7 = -3 × 7

Simplifying: n =

Therefore, n = -21.

Substituting:

n7 = -3

−217 = -3

= -3

vii. 2x3 = 18

Solution:

To isolate x, first multiply both sides by

2x3 × 3 = 18 × 3

2x =

Now divide both sides by 2

2x ÷ 2 = 54 ÷ 2

x =

Therefore, x = 27.

Substituting:

2x3 = 18

2273 = 18

= 18

= 18

viii. 3x + 1 = 16

1 from both sides:

3x + 1 - 1 = 16 - 1

3x =

both sides by :

3x3 = 153

x =

Therefore, the solution is x = 5.

ix. 3p – 7 = 0

Solution:

3p - 7 + 7 = 0 + 7

3p =

3p3 = 73

p =

Therefore, the solution is p = 73.

x. 13 – 6n = 7

Solution:

Subtract from both sides:

13 - 6n - 13 = 7 - 13

-6n =

−6n−6 = −6−6

n =

Therefore, the solution is n = 1.

xi. 200y – 51 = 49

Solution:

200y - 51 + 51 = 49 + 51

200y =

200y200 = 10020050200

y =

Therefore, the solution is y = 12.

xii. 11n + 1 = 1

Solution:

11n + 1 - 1 = 1 - 1

11n =

11n11 = 011

n =

Therefore, the solution is n = 0.

xiii. 7x – 9 = 16

Solution:

7x - 9 + 9 = 16 + 9

7x =

7x7 = 257

x =

Therefore, the solution is x = 257.

xiv. 8x + 52 = 13

Solution:

8x + 52 - 52 = 13 - 52

8x = 13 - 52

8x = - 52

8x =

x = 212 × 18

x =

Therefore, the solution is x = 2116.

xv. 4x - 53 = 9

Solution:

4x - 53 + 53 = 9 + 53

4x = 9 + 53

4x = + 53

4x =

x = 323 × 14

x =

Simplifying: x =

Therefore, the solution is x = 83.

xvi. x + 43 = 312

Solution:

Converting the mixed number to an improper fraction: 3 12 = 3×2+12 =

Rewriting the equation: x + =

Isolating: x = 72 - 43

Finding the common denominator for the fractions: x = () - ()

x =

Therefore, x = 136.