# EXERCISE – 4.3

Q1. Solve the following equations:

(a) 2y + 5/2 = 37/2

SOLUTION:-

= 2y = 37/2 – 5/2

= 2y = 32/2

= 2y = 16

= y = 16/2

= y = 8

(b) 5t + 28 = 10

SOLUTION:-

= 5t = 10 – 28

= 5t = -18

= t = -18/5

(c) a/5 + 3 = 2

SOLUTION:-

= a/5 = 2 – 3

= a/5 = -1

= a = -5

(d) q/4 + 7 = 5

SOLUTION:-

= q/4  = 5 – 7

= q/4 = -2

= q = -8

(e) 5/2 x = -5

SOLUTION:-

= 5x = -5 x 2

= 5x = -10

=

x = -2

(f) 5/2 x = 25/4

SOLUTION:-

=  x = 50/20

= x = 5/2

(g) 7m + 19/2 = 13

SOLUTION:-

= 7m = 13 – (19/2)

= 7m =(26-19)/2

= 7m = 7/2

Now,

Divide both side by 7.

= 7m/7 = (7/2)/7

= m = (7/2) x (1/7)

=m= ½

(h) 6z + 10 = -2

SOLUTION:-

= 6z = -2 -10

= 6z = – 12

= z = -12/6

= z = -2

(i) 3L/2 = 2/3

Solution:-

= L = 2 x2 / 3×3

= L = 4/9

(j) 2b/3 – 5 = 3

SOLUTION:-

= 2b/3 = 3 +5

= 2b/3 = 8

= 2b = 8 x 3

= 2b = 24

= b = 24/2

= b = 12

Q2.Solve the following equations:

(a) 2 ( x + 4 ) = 12

SOLUTION:-

= 2x + 8 = 12

= 2x = 12 – 8

= 2x = 4

= x = 4/2

= x = 2

(b) 3 (n-5) = 21

SOLUTION:-

= 3n – 15 = 21

= 3n = 21 + 15

= 3n = 36

= n = 36/3

= n = 12

(c) 3 (n – 5) = -21

SOLUTION:-

= 3n -15 = -21

= 3n = -21  + 15

= 3n = -6

= n = -6/3

= n = -2

(d) -4 ( 2 +x ) = 8

SOLUTION:-

= -8 + ( -4x) = 8

= -8 – 4x = 8

= -4x = 8 + 8

= -4x = 16

= x = 16/-4

= x = -4

(e) 4(2-x) = 8

SOLUTION:-

= 8 -4x = 8

= -4x = 8 – 8

= -4x = 0

= x = 0/-4

= x = 0

Q3. Solve the following equations:

(a) 4 = 5(p-2)

SOLUTION:-

= 4 = 5p – 10

= 4  = 5p -10

= 4 + 10 = 5p

= 14 = 5p

= 14/5 = p

p = 14/5

(b) -4 = 5(p-2)

SOLUTION:-

= -4 = 5p – 10

= -4 + 10 = 5p

= 6 = 5p

= 6/5 = p

= p = 6/5

(c) 16 = 4 + 3(t+2)

SOLUTION:-

= 16 = 4 + 3t + 6

= 16 = 10 + 3t

= 16 –  10 = 3t

= 6 = 3t

= 6/3 = t

= 2 = t

= t = 2

(d) 4 + 5(p-1) = 34

SOLUTION:-

= 4 + 5p -5 = 34

= 5p = 34 + 5 – 4

= 5p = 35

= p = 35/5

= p = 7

(e) 0 = 16 + 4(m-6)

SOLUTION:-

= 0 = 16 + 4m – 24

= 0 =  16 – 24 + 4m

= 0 = -8 + 4m

= 8 = 4m

= 8/4 = m

= 2 = m

= m = 2

Q4. (a)  Construct 3 equations starting with x = 2

SOLUTION :-

First equation is,

Multiply both side by 6

= 6x = 12 [ equation 1]

Second equation is,

Subtracting 4 from both side ,

= 6x- 4 = 12 – 4

= 6x -4 = 8 [ equation 2]

Thirds equation is,

Divide both side by 6 .

= 6x/6 – (4/6) = (8/6)

= x – (4/6) = (8/6) [ equation 3]

(b) Construct 3 equations starting with x = -2

SOLUTION:-

=First equation is,

Multiply both sides by 5

= 5x = -10 [ equation 1]

Second equation is ,

Subtracting 3 from both sides ,

= 5x – 3 = -10 – 3

= 5x – 3 = -13 [ equation 2]

Third equation is ,

Dividing both sides by 2

= (5x/2) – (3/2) = (-13/2) [ equation 3]