Question

5. Solve the following equations :
(1) 6x + 14 = 16
(iv) 6 (5r-2) + 12 = 30
(ii) 7+ 5x-3x = 21
(v) 7 (x - 4) + 13 = 6
(iii) 1.2x + 4.8x = 18
(vi) 5 (6x+1) = 3(-8+x)+2
12 - x
(ix)
5
(vii) 4 - 4(x - 5) = 2 (2 - x) - 6 (viii) 10 -0.2 (7- y) = 19​

Answer 1

Answer:

1)6x + 14 = 16

=> 6x = 16-14

=> x = 2/6

=> x = 1/3

(iv) 6 (5r-2) + 12 = 30

=> 30r-12+12 = 30

=> 30r = 30

=> r = 1

(ii) 7+ 5x-3x = 21

=> 7+ 2x = 21

=> 2x = 21 - 7

=> x = 14/2

=> x = 7

(v) 7 (x - 4) + 13 = 6

=> 7x-28+13=6

=> 7x-15=6

=> 7x = 6+15

=> x = 21/7

=> x = 3

(iii) 1.2x + 4.8x = 18

=> 6.0x = 18

=> x = 18/6

=> x = 3

(vi) 5 (6x+1) = 3(-8+x)+2

=> 30x+5 = -24+3x+2

=> 30x-3x = -24+2-5

=> 27x = -27

=> x = -1

(vii) 4 - 4(x - 5) = 2 (2 - x) - 6

=> 4-4x+20 = 4-2x-6

=> 24-4x = 10-2x

=> 24-10 = 4x-2x

=> 14 = 2x

=> 2x = 14

=> x = 7

(viii) 10 -0.2 (7- y) = 19

=> 10 - 1.4+0.2y = 19

=> 8.6+0.2y = 19

=> 0.2y = 19-8.6

=> 0.2y = 10.4

=> y = 10.4/0.2

=> y = 104/2

=> y = 52

Answer 2

Step-by-step explanation:

(i) 6x + 14 = 16

6x = 16 - 14

6x = 2

x = 2/6

x = 1/3

(ii) 7 + 5x - 3x = 21

7 + 2x = 21

2x = 21 - 7

2x = 14

x = 14/2

x = 7

(iii) 1.2x + 4.8x = 18

6x = 18

x = 18/6

x = 3

(iv) 6 (5r - 2) + 12 = 30

30r - 12 + 12 = 30

30r = 30

r = 30/30

r = 1

(v) 7 (x - 4) + 13 = 6

7x - 28 + 13 = 6

7x - 15 = 6

7x = 6 + 15

7x = 21

x = 21/7

x = 3

(vi) 5 (6x + 1) = 3(-8 + x)+2

30x + 5 = -24 + 3x + 2

30x - 3x = -24 + 2 - 5

27x = -27

x = -27/27

x = -1

(vii) 4 - 4 (x - 5) = 2 (2 - x) - 6

4 - 4x + 20 = 4 - 2x - 6

24 - 4x = -2 - 2x

24 + 2 = -2x + 4x

26 = 2x

26/2 = x

13 = x

(viii) 10 - 0.2 (7- y) = 19

10 - 1.4 + 0.2y = 19

8.6 + 0.2y = 19

0.2y = 19 - 8.6

0.2y = 10.4

y = 10.4/0.2

y = 52